{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 } {CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "2 D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE "" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 }{CSTYLE "Help Normal" -1 30 "Times" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 256 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "Helvet ica" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "Helvetica" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "Helveti ca" 1 14 128 0 128 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 268 "Helvetica" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "Helvetica" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "Helvetica" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "Hel vetica" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "Helvetica" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "Courier" 0 18 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 276 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 277 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 278 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "Courier" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "Courier" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 283 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "Cour ier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 290 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 291 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 292 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 293 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 294 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 296 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 297 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 298 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 299 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 300 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 301 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 302 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 303 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 304 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 305 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 306 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 307 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 308 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 309 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 310 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 311 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 312 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 313 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 314 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 315 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 316 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 317 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 318 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 319 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 320 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 321 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 322 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 323 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 324 "" 1 10 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 325 "" 1 10 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 326 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 327 "Helvetica" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 328 "Helvetica" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 329 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 }{CSTYLE "" -1 330 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 331 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 332 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 333 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 334 "Helvetic a" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 335 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 336 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 337 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 338 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 339 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 340 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 341 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 342 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 343 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 344 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 345 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 346 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 347 "Helvetic a" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 348 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 349 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 350 "Helvetica" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 351 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 352 "Helvetica" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 353 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 354 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 355 "Helvetica" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 356 "Helvet ica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 357 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 358 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 359 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 360 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 361 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 362 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 363 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 364 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 365 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 366 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 367 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 368 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 369 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 370 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 371 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 372 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 373 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 374 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 375 "" 1 18 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 376 "" 1 18 128 0 128 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 377 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 378 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 379 "Helvetic a" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 380 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 381 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 382 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 383 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 384 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 385 "" 1 18 128 0 128 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 386 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 387 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 388 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" 18 389 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 390 "Helvetica" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 391 "Hel vetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 392 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 393 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 394 "Helvetica" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 395 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 396 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 397 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 398 "Helvetic a" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 399 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 400 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 401 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 402 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 403 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 404 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 405 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 406 "Helvetic a" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 407 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 18 408 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 409 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 410 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 411 "H elvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 412 "Courier" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 413 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 414 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 415 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 416 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 417 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 418 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 419 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 420 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 421 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 422 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 423 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 424 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 425 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 426 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 427 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 428 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 429 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 430 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 431 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 432 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 433 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 434 "C ourier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 435 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 436 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 437 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 438 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 439 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 440 "" 1 14 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 441 "" 1 14 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 442 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 443 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 444 "Courier" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 445 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 446 "Helvetica" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 447 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 448 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 449 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 450 "Helvetic a" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 451 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 452 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 453 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 454 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 455 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 456 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 457 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 458 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 459 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 460 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 461 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 462 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 463 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 464 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 465 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 466 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 467 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 468 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 469 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 470 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 471 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 472 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 473 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE " " -1 474 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 475 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 476 "Courier " 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 477 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 478 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 479 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 480 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 481 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 482 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 483 "" 1 14 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 484 "Helveti ca" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 485 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 486 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 487 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 488 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 489 "" 1 14 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 490 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 491 "Cour ier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 492 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 493 "" 1 14 255 0 255 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 494 "" 1 14 255 0 255 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 495 "Times" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 496 "Courier" 1 18 0 0 0 0 0 0 0 0 0 0 3 0 0 }{CSTYLE "" -1 497 "Courier" 1 18 0 0 0 0 0 0 0 0 0 0 3 0 0 }{CSTYLE "" -1 498 "Courier" 0 1 255 0 0 1 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 499 "Courier" 0 1 255 0 0 1 2 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 500 "" 1 14 255 0 255 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 501 "Courier" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 502 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 503 "Helvetica" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 504 "Helvetica" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 505 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 506 "" 1 14 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 507 "" 1 14 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 508 "" 1 14 0 0 0 0 1 0 1 0 0 0 0 0 0 } {CSTYLE "" -1 509 "Courier" 0 1 255 0 0 1 0 1 0 0 0 0 0 0 0 }{PSTYLE " Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Couri er" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output " -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }1 1 0 0 3 3 1 0 1 0 2 2 15 2 }{PSTYLE "R3 Font 2 " -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Author" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 1 0 0 8 8 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 260 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 261 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 262 1 {CSTYLE "" -1 -1 "Helvetica" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 }1 1 0 0 6 6 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 263 1 {CSTYLE "" -1 -1 "Helvetica" 1 18 0 0 0 1 2 2 2 2 2 2 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT 256 51 "First Order Differentia l Equations\nAssorted Methods" }}{PARA 258 "" 0 "" {TEXT 257 14 "Brian E. Blank" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 256 "" 0 " " {TEXT -1 83 "Click on a [+] sign to expand a section. Click on a [-] sign to collapse a section." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 "I " }{TEXT 488 11 "ntroduction" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 335 7 "In this" }{TEXT -1 2 " " }{TEXT 258 5 "MAPLE" }{TEXT -1 4 " " }{HYPERLNK 17 "worksheet" 2 "worksheet" "" }{TEXT 334 14 ", we will use" }{TEXT -1 2 " " }{TEXT 259 5 "MAPLE" }{TEXT -1 3 " " }{TEXT 333 75 "to implement several methods of solving firs t order differential equations." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 259 "" 0 "" {TEXT 503 9 "Key Words" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 152 "The w ords and symbols that are used in this worksheet have been collected h ere as hypertext links. Click on any word to go to the correspond help page." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "Dchangevar" 2 "Dchangevar" "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "DEt ools" 2 "DEtools" "" }{TEXT -1 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 " dfieldplot" 2 "dfieldplot" "" }{TEXT -1 3 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "diff" 2 "diff" "" }{TEXT 496 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "display" 2 "display" "" }{TEXT -1 1 " " }{TEXT 497 1 " \+ " }}{PARA 15 "" 0 "" {HYPERLNK 17 "dsolve" 2 "dsolve" "" }{TEXT -1 2 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "for" 2 "for" "" }{TEXT -1 1 " " } }{PARA 15 "" 0 "" {HYPERLNK 17 "implicitplot" 2 "implicitplot" "" } {TEXT -1 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "int" 2 "int" "" }} {PARA 15 "" 0 "" {HYPERLNK 17 "LambertW" 2 "LambertW" "" }}{PARA 15 " " 0 "" {HYPERLNK 17 "loop" 2 "loop" "" }{TEXT -1 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "lists" 2 "lists" "" }{TEXT -1 2 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "normal" 2 "normal" "" }{TEXT -1 3 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "odeadvisor" 2 "odeadvisor" "" }{TEXT -1 1 " " }} {PARA 15 "" 0 "" {HYPERLNK 17 "odetest" 2 "odetest" "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "op" 2 "op" "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "pack ages" 2 "packages" "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "plot" 2 "plot" "" }{TEXT 329 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "plots" 2 "plots" "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "plot,structure" 2 "plot,structure " "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "restart" 2 "restart" "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "selection" 2 "selection" "" }}{PARA 15 "" 0 " " {HYPERLNK 17 "solve" 2 "solve" "" }{TEXT -1 1 " " }}{PARA 15 "" 0 " " {HYPERLNK 17 "subs" 2 "subs" "" }{TEXT -1 1 " " }}{PARA 15 "" 0 "" {HYPERLNK 17 "value" 2 "value" "" }}{PARA 15 "" 0 "" {HYPERLNK 17 "wit h\n" 2 "with" "" }}{PARA 0 "" 0 "" {TEXT 332 34 "On-line information a bout using a " }{TEXT 328 6 " MAPLE" }{TEXT -1 2 " " }{TEXT 330 59 "f unction can also be obtained at a prompt by preceding the " }{TEXT 327 5 "exact" }{TEXT 331 52 " keyword by a question mark and executing that line." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 " " {TEXT 502 5 "Lists" }}{PARA 0 "" 0 "" {TEXT -1 89 "In this worksheet we will see several functions that return each several data items. I n " }{TEXT 504 5 "MAPLE" }{TEXT -1 5 " a " }{HYPERLNK 17 "list" 2 "l ist" "" }{TEXT -1 114 " is an ordered sequence enclosed in square bra ckets. For example, the list of square integers less than fifty is:" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "A := [seq(k^2, k = 1..7)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"AG7)\"\"\"\"\"%\"\"*\"#;\"#D\"#O\"#\\" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 58 "If we want to select the j'th elem ent we use the syntax " }{TEXT 505 4 "A[j]" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "A[6 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#O" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 297 "Many of the functions that wil l be given in this worksheet return a list of steps that are taken to \+ implement a particular differential equation solving procedure. Since \+ the last entry is the solution itself, it is convenient to have a func tion that extracts that entry. Here is such a function:\n\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 201 "lastEntry := proc()\n \+ if nargs = 1 and type(args[1], list) then\n RETURN( args[1 ][nops(args[1])] );\n else\n RETURN(args);\n \+ fi:\n end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "lastEntry(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"# \\" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 262 "" 0 "" {TEXT -1 20 "Homgeneous Equations" }}{SECT 0 {PARA 4 "" 0 "" {TEXT 358 6 "Theor y" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 77 " S uppose that we are to solve a first order differential equation of the form" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 336 24 "y '(x) = F( x , y(x) ). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT 342 19 "If the expression " }{TEXT -1 1 " " }{TEXT 337 15 " F( x , y(x) ) " }{TEXT -1 2 " " }{TEXT 343 19 "can be expressed \+ as" }{TEXT -1 2 " " }{TEXT 338 13 "Q( y(x)/x ) " }{TEXT -1 1 " " } {TEXT 344 23 " then the substitution " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 339 13 "v(x) = y(x)/x" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 346 45 "leads to a first order s eparable equation for" }{TEXT -1 2 " " }{TEXT 341 1 "v" }{TEXT -1 1 " " }{TEXT 345 17 " as a function of" }{TEXT -1 2 " " }{TEXT 340 1 "x " }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 276 7 "Example" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 277 30 "Solve th e homogeneous equation" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 23 " " } {XPPEDIT 278 0 "`y'(x)` = x*y/(x^2+y^2);" "/%&y'(x)G*(%\"xG\"\"\"%\"yG F&,&*$F%\"\"#F&*$F'F*F&!\"\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 279 9 "Solution:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "restart: with( plots ): with( DEtools ):" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "diff_eq := d iff(y(x),x) = x*y(x)/(x^2+y(x)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%(diff_eqG/-%%diffG6$-%\"yG6#%\"xGF,*(F,\"\"\"F)F.,&*$F,\"\"#F.*$F)F1 F.!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 347 96 "Like many differential equations, this equation falls under severa l types in the classification." }{TEXT -1 1 "\n" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 22 "dsolve(diff_eq, y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&%\"xG\"\"#-%\"yG6#F&!\"##!\"\"F'-%#lnG6#F(\"\"\"%$ _C1G" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 348 3 "So " }{TEXT 352 5 "MAPLE" }{TEXT -1 1 " " }{TEXT 353 56 " has found a solution - i t involves a special function, " }{HYPERLNK 17 "LambertW" 2 "LambertW " "" }{TEXT 349 20 ", that is known to " }{TEXT 350 5 "MAPLE" }{TEXT -1 1 " " }{TEXT 351 31 ". \nLet us verify the solution:" }{TEXT -1 1 "\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "y(x) = solve(\" , y(x ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG-%$expG6#,&-%)Lam bertWG6#*&F'\"\"#-F)6#,$%$_C1G!\"#\"\"\"#F6F0F4F6" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "subs(\", dif f_eq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%diffG6$-%$expG6#,&-%)Lam bertWG6#*&%\"xG\"\"#-F(6#,$%$_C1G!\"#\"\"\"#F6F0F4F6F/*(F/F6F'F6,&*$F/ F0F6*$F'F0F6!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simpli fy(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*,-%)LambertWG6#*&%\"xG\" \"#-%$expG6#,$%$_C1G!\"#\"\"\"F1,&F1F1F%F1!\"\"F)F3-F,6#F/F1*(F)F*F+F1 F%F3#F1F*F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "testeq(\"); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{PARA 0 "" 0 "" {TEXT 354 27 "\nNow let us see how to use " }{TEXT 355 6 " MAPLE" }{TEXT 356 54 " to solve the the differential equation step-by-step:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "diff_eq2 := Dchangevar(y(x)=x*v(x), [diff_eq], x );" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%)diff_eq2G/,&-%\"vG6#%\"xG\"\"\"*&F*F+-%%diffG 6$F'F*F+F+*(F*\"\"#F'F+,&*$F*F1F+*&F*F1F'F1F+!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "diff_eq3 := diff(v(x),x) = solve(diff_eq2, \+ diff(v(x),x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)diff_eq3G/-%%diff G6$-%\"vG6#%\"xGF,,$*(F)\"\"$F,!\"\",&\"\"\"F2*$F)\"\"#F2F0F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "diff_eq4 := lhs(diff_eq3) = \+ normal(rhs(diff_eq3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)diff_eq4G /-%%diffG6$-%\"vG6#%\"xGF,,$*(F)\"\"$F,!\"\",&\"\"\"F2*$F)\"\"#F2F0F0 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "int((1+v^2)/v^3,v) = in t(-1/x,x)+C;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&-%#lnG6#%\"vG\"\"\" *$F(!\"##!\"\"\"\"#,&-F&6#%\"xGF-%\"CGF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "subs(v = y(x)/x, \");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&-%#lnG6#*&-%\"yG6#%\"xG\"\"\"F,!\"\"F-*&F)!\"#F,\"\"##F.F1,&- F&F+F.%\"CGF-" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 361 57 "Notice that this is the same solution as was obtained by " }{TEXT 365 8 " dsolve " }{TEXT 366 7 "(with " }{TEXT 367 2 "C " } {TEXT 368 12 "instead of " }{TEXT 369 4 " _C1" }{TEXT 370 65 "). \n\n After the next section we will give the code for a function," }{TEXT -1 1 " " }{TEXT 357 15 "homogeneous_ode" }{TEXT -1 2 ", " }{TEXT 362 106 "that performs each of these steps in an automated fashion, and re ports the results of the principal steps." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 363 8 "Graphics" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 364 103 "In this subsection w e will plot some solution curves and superimpose them on the direction field plot. " }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "direction_field_plot := dfieldplot( [diff_eq] , [y(x )], x = -5 .. 5 , y = 0 .. 4 ,color = COLOR(RGB,0.7,0.85,0.75)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "display(direction_field_plot );" }}{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6]dl7%7$$!+&*y:j_!\"*\"\" !7$$!+0@%ot%F*F+7$$!+;Gz][F*$\"+[*y:j#!#67%7$$!+1@%ot%F*F+7$$!+;j_5UF* F+7$$!+FqZCVF*F27%7$$!+AF*F27%7$$!+ hJE0@F*F+7$$!+rt%*y:F*F+7$$!+#3)*Gp\"F*F27%7$$!+st%*y:F*F+7$$!+#eJE0\" F*F+7$$!+$H#em6F*F27%F_p7$$!+Fz:j_!#5F+7$$!+Q]m-kFipF27%7$$!+Gz:j_FipF +7$$!#KFipF+7$$!+Vr]R6FipF27%7$$!#LFipF+7$$\"+jy:j_FipF+7$$\"+_2lBTFip F27%7$$\"+iy:j_FipF+7$$\"+w:j_5F*F+7$$\"+\\'3oQ*FipF27%Fer7$$\"+mt%*y: F*F+7$$\"+bm*\\Y\"F*F27%F\\s7$$\"+cJE0@F*F+7$$\"+XCJ\"*>F*F27%Fcs7$$\" +Y*y:j#F*F+7$$\"+N#Gw^#F*F27%Fjs7$$\"+OZ*y:$F*F+7$$\"+DS%R/$F*F27%Fat7 $$\"+E0@%o$F*F+7$$\"+:)f-d$F*F27%Fht7$$\"+;j_5UF*F+7$$\"+0cd'4%F*F27%F _u7$$\"+1@%ot%F*F+7$$\"+&R\"*Gi%F*F27%Ffu7$$\"+'*y:j_F*F+7$$\"+&=2#\\^ F*F27%7$$!+Lqrh_F*$\"+(yk_@#Fip7$$!+nHGQZF*$\"+H:E&*>Fip7$$!+lYtW[F*$ \"+k1h/BFip7%7$$!+4v/NZF*$\"+ye)zA#Fip7$$!+84K7UF*$\"+Q/a#)>Fip7$$!+rV #yJ%F*$\"+KU/(H#Fip7%7$$!+w2B3UF*$\"+J^*RC#Fip7$$!+og]'o$F*$\"+&=Jl'>F ip7$$!+K?z!z$F*$\"+XiY(G#Fip7%7$$!+(4t6o$F*$\"+zLtkAFip7$$!+p@$4;$F*$ \"+QHzX>Fip7$$!+X2gjKF*$\"+Lg'\\F#Fip7%7$$!+nMp`JF*$\"+_Vg#H#Fip7$$!+@ -yNEF*$\"+l>#z\">Fip7$$!+.H?OFF*$\"+/(**zD#Fip7%7$$!+PoSDEF*$\"+>U!>L# Fip7$$!+u_V6@F*$\"+(4A'y=Fip7$$!+:$[&3AF*$\"+PjuLAFip7%7$$!+kGQ&4#F*$ \"+58*4R#Fip7$$!+ow#))e\"F*$\"+1]`>=Fip7$$!+w?k!o\"F*$\"+Bl`'>#Fip7%7$ $!+M/'4c\"F*$\"+\\^u([#Fip7$$!+?&=12\"F*$\"+n6yAHFip7$$!*#[[H'*Fip$\"+kqH \"H\"Fip7$$!+tyvw6Fip$\"+sxh5=Fip7%7$$\"*A%[H'*Fip$\"+iqH\"H\"Fip7$$\" +3%4-I%Fip$\"+a#H#>HFip7$$\"+*RU*oIFip$\"+XYjLFFip7%7$$\"+j@cgcFip$\"+ .r.\\:Fip7$$\"+Y6*G,\"F*$\"+8#*[hEFip7$$\"+vT%Q\"))Fip$\"+JP0WEFip7%7$ $\"+:&=12\"F*$\"+m6yAF*$\"+*)\\a?DFip7%7$$\"+q_V6@F*$\"+'4A'y=Fip7$$\"+LoSDEF*$\"+?U!>L# Fip7$$\"+fO'**\\#F*$\"+V:v!\\#Fip7%7$$\"+=-yNEF*$\"+k>#z\">Fip7$$\"+kM p`JF*Fgz7$$\"+LJ&)HIF*$\"+e)R/Z#Fip7%7$$\"+n@$4;$F*$\"+PHzX>Fip7$$\"+& 4t6o$F*Fgy7$$\"+T2deNF*$\"+77!eX#Fip7%7$$\"+ng]'o$F*F\\y7$$\"+v2B3UF*F gx7$$\"+9Lg'3%F*$\"+yZyWCFip7%7$$\"+84K7UF*F\\x7$$\"+4v/NZF*Fgw7$$\"+6 P?9YF*$\"+z'3iV#Fip7%7$$\"+oHGQZF*F\\w7$$\"+Mqrh_F*Fgv7$$\"+L^^T^F*$\" +<(\\$HCFip7%7$$!+@)*ed_F*$\"+Qm\"fU%Fip7$$!+!=5Cu%F*$\"+%*f8&*RFip7$$ !+\\z[S[F*$\"+gD*fM%Fip7%7$$!+xT'*HZF*$\"+GJh\\WFip7$$!+XUSCGJ%Fip7%7$$!+Ai*Gn$F*$\"+YC'e^%Fip 7$$!+X!4#pJF*$\"+'=!>0RFip7$$!+5q[#*G%Fip7%7$$!+l_kUJF*$\"+ ]$\\Oc%Fip7$$!+B%Gok#F*$\"+#G.u&QFip7$$!+Hd5KFF*$\"+i%=#eUFip7%7$$!+7M 55EF*$\"+j0-FYFip7$$!+*pQn7#F*$\"+p?.%z$Fip7$$!+R$f`?#F*$\"+D<1;UFip7% 7$$!+RJOt?F*$\"+-3(Gr%Fip7$$!+$RZ3h\"F*$\"+I==3PFip7$$!+f%)ez;F*$\"+Y7 'p:%Fip7%7$$!+e]xG:F*$\"+K=xG[Fip7$$!+'*Q!G5\"F*$\"++3G#f$Fip7$$!+8!*Q c6F*$\"+UX(H2%Fip7%7$$!+7RZ?(*Fip$\"+yho\\Fip7$$\"+G$*4c%)Fip$\"+s #GH#[Fip7%7$$\"+!*Q!G5\"F*$\"+)z!G#f$Fip7$$\"+_]xG:F*$\"+M=xG[Fip7$$\" +X#4zR\"F*$\"+_#\\Sx%Fip7%7$$\"+*QZ3h\"F*$\"+H==3PFip7$$\"+MJOt?F*$\"+ .3(Gr%Fip7$$\"+2!H=%>F*$\"+KrgEZFip7%7$$\"+&pQn7#F*$\"+o?.%z$Fip7$$\"+ 2M55EF*$\"+k0-FYFip7$$\"+')4UzCF*$\"+@cN)o%Fip7%7$$\"+?%Gok#F*Fj]m7$$ \"+i_kUJF*Fe]m7$$\"+xvA8IF*$\"+75leYFip7%7$$\"+V!4#pJF*Fj\\m7$$\"+?i*G n$F*Fe\\m7$$\"+R7wWNF*$\"+7;\\NYFip7%7$$\"++m'Fip7$$!+T_*\\A% F*$\"+K*f:(fFip7$$!+yj;6VF*$\"+nYIpjFip7%7$$!+z$RD>%F*$\"+m9F)p'Fip7$$ !+mu>-PF*$\"+$[2L$fFip7$$!+![aWy$F*$\"++!)4WjFip7%7$$!+:7OhOF*$\"+BP\" [u'Fip7$$!+^Su!=$F*$\"+E_w')eFip7$$!+/n)zD$F*$\"+dn%GJ'Fip7%7$$!+-5:GJ F*$\"+@b\">!oFip7$$!+'oA8m#F*$\"+FMmHeFip7$$!+.6,KFF*$\"+QjdtiFip7%7$$ !+?&Q=f#F*$\"+Gb,soFip7$$!+!f.]9#F*$\"+@McfdFip7$$!+i?)p?#F*$\"+KQ$QA' Fip7%7$$!+Fr\"40#F*$\"+H-TcpFip7$$!+1MHL;F*$\"+>(o^n&Fip7$$!+(zsOo\"F* $\"+.vPhhFip7%7$$!+8I=/:F*$\"+[Zu]qFip7$$!+UfRF6F*$\"++U$3e&Fip7$$!+J! QI;\"F*$\"+/FZ(3'Fip7%7$$!+rtOj&*Fip$\"+pbvHrFip7$$!+zj5EiFip$\"+zL#=] &Fip7$$!+pd\"*RkFip$\"+(3W6-'Fip7%7$$!+J,t*f%Fip$\"+o8a9qFip7$$!*HyUj' Fip$\"+!ePqh&Fip7$$!+VB%*y5Fip$\"+T6U;hFip7%7$$\"*]xUj'Fip$\"+(ePqh&Fi p7$$\"+!3I(*f%Fip$\"+h8a9qFip7$$\"+(pv2J$Fip$\"+N!)y3pFip7%7$$\"+:j5Ei FipFfdn7$$\"+0tOj&*Fip$\"+qbvHrFip7$$\"+'H+@L)Fip$\"+h4;WpFip7%7$$\"+O fRF6F*$\"+*>M3e&Fip7$$\"+1I=/:F*$\"+\\Zu]qFip7$$\"+3:nw8F*$\"+:L*3#pFi p7%7$$\"+,MHL;F*$\"+=(o^n&Fip7$$\"+@r\"40#F*$\"+I-TcpFip7$$\"+O,Y?>F*$ \"+m^#y)oFip7%7$$\"+'e.]9#F*$\"+?McfdFip7$$\"+;&Q=f#F*Faan7$$\"+(yJ.Y# F*$\"+Y+eaoFip7%7$$\"+$oA8m#F*Ff`n7$$\"+**4:GJF*Fa`n7$$\"+Eop'*HF*$\"+ E4$[#oFip7%7$$\"+\\Su!=$F*$\"+D_w')eFip7$$\"+87OhOF*Fa_n7$$\"+H0\\INF* $\"+c$\\$*z'Fip7%7$$\"+lu>-PF*Ff^n7$$\"+y$RD>%F*Fa^n7$$\"+:@ZiSF*$\"+i G#yx'Fip7%7$$\"+T_*\\A%F*Ff]n7$$\"+\"=tBs%F*Fa]n7$$\"+_L<$f%F*$\"+AAlf nFip7%7$$\"+q=q[ZF*Ff\\n7$$\"+K\")H^_F*Fa\\n7$$\"+-^&H7&F*$\"+k$RUu'Fi p7%7$$!+,``V_F*$\"+zO!*>))Fip7$$!+*pkkv%F*$\"+&e,A-)Fip7$$!+(Q!*p$[F*$ \"+bWWQ%)Fip7%7$$!+?)fKr%F*$\"+Akec))Fip7$$!+-'3TB%F*$\"+U)=b)zFip7$$! +Aqi5VF*$\"+9ho8%)Fip7%7$$!+twy\"=%F*$\"+>zP**))Fip7$$!+r\"\\Hr$F*$\"+ YtsUzFip7$$!+a.c%y$F*$\"+@vE%Q)Fip7%7$$!+I*p'[OF*$\"+4?L\\*)Fip7$$!+O` V$>$F*$\"+bKx#*yFip7$$!+c!z*eKF*$\"+KA9\\$)Fip7%7$$!+:sI8JF*$\"+Q=;#F*$\"+*or*oxFip7$$!+Oh`5AF*$\"+&)Q\"zD)Fip7%7$$!+ M@ML?F*$\"+-I;W\"*Fip7$$!+)Ro3l\"F*$\"+iA%zp(Fip7$$!+$*>[)o\"F*$\"+0^H -#)Fip7%7$$!+x,v*[\"F*$\"+\\b)3@*Fip7$$!+x(G=9\"F*$\"+:(>7j(Fip7$$!+79 zn6F*$\"+,\")=Z\")Fip7%7$$!+(*pvS&*Fip$\"+`;NU#*Fip7$$!+`nr[iFip$\"+6O v*f(Fip7$$!+&[_\"[kFip$\"+J&))*>\")Fip7%7$$!+WubvZFip$\"+mzVJ!*Fip7$$! *;0g([Fip$\"+)Hn1\"yFip7$$!+!fzW.\"Fip$\"+Z(p$*G)Fip7%7$$\"*O/g([Fip$ \"+1tm5yFip7$$\"+%Rdbx%Fip$\"+ezVJ!*Fip7$$\"+^mplMFip$\"+27`\")*)Fip7% 7$$\"+)o;([iFipF`go7$$\"+KpvS&*FipF[go7$$\"+Bup9$)Fip$\"+d2K^!*Fip7%7$ $\"+r(G=9\"F*$\"+9(>7j(Fip7$$\"+r,v*[\"F*$\"+]b)3@*Fip7$$\"+@%e]O\"F*$ \"+k&QG/*Fip7%7$$\"+$Ro3l\"F*$\"+hA%zp(Fip7$$\"+H@ML?F*$\"+.I;W\"*Fip7 $$\"+Q(R`!>F*$\"+&*QGA!*Fip7%7$$\"+'=Q=;#F*F`do7$$\"+;R+vDF*F[do7$$\"+ _ezWCF*$\"+4rN(**)Fip7%7$$\"+qk;wEF*$\"+ZI#[$yFip7$$\"+7sI8JF*F[co7$$ \"+;T-#)HF*$\"+Kx+s*)Fip7%7$$\"+M`V$>$F*F`bo7$$\"+G*p'[OF*F[bo7$$\"+'G \"4[*)Fip7%7$$\"+q\"\\Hr$F*$\"+XtsUzFip7$$\"+swy\"=%F*F[ao7 $$\"+HeQ]SF*$\"+XinE*)Fip7%7$$\"+-'3TB%F*F``o7$$\"+?)fKr%F*F[`o7$$\"+w '*H#e%F*$\"+o.d2*)Fip7%7$$\"++ZYcZF*F`_o7$$\"+-``V_F*F[_o7$$\"+LK:8^F* $\"+59t!*))Fip7%7$$!+#Q+]B&F*$\"+hc++6F*7$$!+='**\\w%F*$\"+(\\d_+\"F*7 $$!+n*[r$[F*$\"+:6F\\5F*7%7$$!+Hwa.ZF*$\"+<)zQ5\"F*7$$!+$z?QC%F*$\"+TL Q,5F*7$$!+CWK6VF*$\"+@3cY5F*7%7$$!+()eyqTF*$\"+%=a#36F*7$$!+d4&Rs$F*$ \"+O(*3q**Fip7$$!+H%Hfy$F*$\"+:gVV5F*7%7$$!+PiOOOF*$\"+g@:86F*7$$!+H!R d?$F*$\"+$)*46#**Fip7$$!+#>Z6E$F*$\"+R&[)R5F*7%7$$!+dg$**4$F*$\"+w\\`= 6F*7$$!+Jw`*o#F*$\"+A=Gn)*Fip7$$!+u=?PFF*$\"+6^yN5F*7%7$$!+mALhDF*$\"+ #\\FU7\"F*7$$!+W)4b<#F*$\"+emN5)*Fip7$$!+.aH9AF*$\"+F(G8.\"F*7%7$$!+X8 <@?F*$\"+OxwH6F*7$$!+(=RIm\"F*$\"+?U&\\v*Fip7$$!+wpO#p\"F*$\"+mH!o-\"F *7%7$$!+FDl#[\"F*$\"+*=GS8\"F*7$$!+Fk#*[6F*$\"+&p\\Br*Fip7$$!+mtIq6F*$ \"+Sq;B5F*7%7$$!+iEVz&*Fip$\"+xp\\L6F*7$$!+)3T+@'Fip$\"+6=m<(*Fip7$$!+ Eq7MkFip$\"+$))GO-\"F*7%7$$!+2p#)**[Fip$\"+>@+16F*7$$!*`5Lj$Fip$\"+*Q5 E***Fip7$$!+T`%>,\"Fip$\"+SO0X5F*7%7$$\"*u4Lj$Fip$\"+)R5E***Fip7$$\"+c o#)**[Fip$\"+=@+16F*7$$\"+;33%e$Fip$\"+wWd06F*7%7$$\"+?5/5iFip$\"+7=m< (*Fip7$$\"++EVz&*FipFcip7$$\"+)=HXM)Fip$\"+!>G`6\"F*7%7$$\"+Ak#*[6F*Fh hp7$$\"+@Dl#[\"F*Fchp7$$\"+?e_f8F*$\"+G(oa6\"F*7%7$$\"+#=RIm\"F*Fhgp7$ $\"+S8<@?F*Fcgp7$$\"+bLU&*=F*$\"+3MF96F*7%7$$\"+T)4b<#F*Fhfp7$$\"+hALh DF*Fcfp7$$\"+6=0LCF*$\"+tm^76F*7%7$$\"+Gw`*o#F*Fhep7$$\"+ag$**4$F*Fcep 7$$\"+mD*)pHF*$\"+*)y^56F*7%7$$\"+F!Rd?$F*Fhdp7$$\"+NiOOOF*Fcdp7$$\"+Y tI0NF*$\"+StZ36F*7%7$$\"+c4&Rs$F*Fhcp7$$\"+')eyqTF*Fccp7$$\"+d\"z#RSF* $\"+O1^16F*7%7$$\"+$z?QC%F*Fhbp7$$\"+Hwa.ZF*Fcbp7$$\"+,P)>d%F*$\"+@]n/ 6F*7%7$$\"+>'**\\w%F*Fhap7$$\"+$Q+]B&F*Fcap7$$\"+JMj.^F*$\"+?@*H5\"F*7 %7$$!+2PGE_F*$\"+yY*oJ\"F*7$$!+$H;Px%F*$\"+76U47F*7$$!+BX6Q[F*$\"+#>=` D\"F*7%7$$!+Gy%Rp%F*$\"+=zv?8F*7$$!+%f?MD%F*$\"+syb07F*7$$!+Cvz7VF*$\" +vd__7F*7%7$$!+.SNgTF*$\"+ZC)\\K\"F*7$$!+TGQMPF*$\"+VLL,7F*7$$!+ez'zy$ F*$\"+&z;KF*$\"+`!)y'>\"F*7$$! +1,wjKF*$\"+#y_fC\"F*7%7$$!+u$\\()3$F*$\"+ogFM8F*7$$!+9Vs+FF*$\"+A(R?> \"F*7$$!+Y`GSFF*$\"+ZgBU7F*7%7$$!+fZ*4b#F*$\"+Xq'*Q8F*7$$!+^t%e=#F*$\" +X([t=\"F*7$$!+lL_XhFip$\"+Gm_%=\"F*7$$!+p7K6kFip$\"+A/2O7F*7%7$$!+ fx6')\\Fip$\"+<.<58F*7$$!*,-/x#Fip$\"+ta9;7F*7$$!+hxv-5Fip$\"+Py/g7F*7 %7$$\"*C,/x#Fip$\"+ua9;7F*7$$\"+1x6')\\Fip$\"+;.<58F*7$$\"+p[usOFip$\" +G(eLJ\"F*7%7$$\"+76>XhFipFf[r7$$\"+3DGW'*FipFa[r7$$\"+y:E&R)Fip$\"+#G O_K\"F*7%7$$\"+XDJ^6F*Ffjq7$$\"+(Rm-[\"F*Fajq7$$\"+c&*od8F*$\"+F\\>E8F *7%7$$\"+W&*yq;F*Ffiq7$$\"+y4U8?F*Faiq7$$\"+d(*H*)=F*$\"+@MfD8F*7%7$$ \"+[t%e=#F*Ffhq7$$\"+bZ*4b#F*Fahq7$$\"+.tbCCF*$\"+!4)RC8F*7%7$$\"+6Vs+ FF*Ffgq7$$\"+r$\\()3$F*Fagq7$$\"+B1HgHF*$\"+\\A)GK\"F*7%7$$\"+)=&z;KF* Fffq7$$\"+u+JDOF*Fafq7$$\"+bGQ&\\$F*$\"+(\\97K\"F*7%7$$\"+SGQMPF*Ffeq7 $$\"+-SNgTF*Faeq7$$\"+&>)[HSF*$\"+*=5&>8F*7%7$$\"+%f?MD%F*Ffdq7$$\"+Gy %Rp%F*Fadq7$$\"+q3diXF*$\"+QF%yJ\"F*7%7$$\"+%H;Px%F*Ffcq7$$\"+3PGE_F*F acq7$$\"+*\\9Z4&F*$\"+RVD;8F*7%7$$!+u(>y@&F*$\"+vCvK:F*7$$!+E-=#y%F*$ \"+Zfh99F*7$$!+!H\"eR[F*$\"+L_(>Y\"F*7%7$$!+?o#\\o%F*$\"+m#ek`\"F*7$$! +-;WiUF*$\"+c,\"4T\"F*7$$!+]&yYJ%F*$\"+!Q;#f9F*7%7$$!+5P%4:%F*$\"+\\&) QS:F*7$$!+MJzVPF*$\"+t)zpS\"F*7$$!+3OD!z$F*$\"+G7Ac9F*7%7$$!+wS%eh$F*$ \"+)*3YW:F*7$$!+!>hiA$F*$\"+Cv!HS\"F*7$$!+HHPmKF*$\"+tQ.`9F*7%7$$!+,)= )zIF*$\"+\")Q^[:F*7$$!+))[l4FF*$\"+TX&))R\"F*7$$!+#=HIu#F*$\"+M\\w\\9F *7%7$$!+,pcVDF*$\"+#F*$\"+067&R\"F*7$$!+VO,?AF*$\"+7X lY9F*7%7$$!+;$o*3?F*$\"+@33b:F*7$$!+;ACv;F*$\"+,wG#R\"F*7$$!+bJi'p\"F* $\"+s'>UW\"F*7%7$$!+!*[#3[\"F*$\"+N[nb:F*7$$!+kSv]6F*$\"+(e$p\"R\"F*7$ $!+aB(4<\"F*$\"+5,qV9F*7%7$$!+e#H\"=(*Fip$\"+(f$e\\:F*7$$!+#\\W82'Fip$ \"+D[y(R\"F*7$$!+$RDlQ'Fip$\"+ZT))[9F*7%7$$!+Ae\"o/&Fip$\"+Y1[::F*7$$! *Q@M;#Fip$\"+wx)=V\"F*7$$!+[E%4+\"Fip$\"+K&QTZ\"F*7%7$$\"*k?M;#Fip$\"+ xx)=V\"F*7$$\"+md\"o/&Fip$\"+X1[::F*7$$\"+:)f(RPFip$\"+EY`@:F*7%7$$\"+ BWMrgFipFb]s7$$\"+(>H\"=(*FipF]]s7$$\"+tf?a%)Fip$\"+B@&\\`\"F*7%7$$\"+ eSv]6F*Fb\\s7$$\"+%)[#3[\"F*F]\\s7$$\"+9$=\"e8F*$\"+&Rvm`\"F*7%7$$\"+7 ACv;F*Fb[s7$$\"+6$o*3?F*F][s7$$\"+5;%e)=F*$\"+g8_O:F*7%7$$\"+1_F$>#F*F bjr7$$\"+(*ocVDF*F]jr7$$\"+!eC'=CF*$\"+zIuN:F*7%7$$\"+&)[l4FF*Fbir7$$ \"+(z=)zIF*F]ir7$$\"+:u!H&HF*$\"+z)>Y`\"F*7%7$$\"+*=hiA$F*Fbhr7$$\"+uS %eh$F*F]hr7$$\"+w9E([$F*$\"+QGHL:F*7%7$$\"+LJzVPF*Fbgr7$$\"+4P%4:%F*F] gr7$$\"+7G5@SF*$\"+_A'=`\"F*7%7$$\"+-;WiUF*Fbfr7$$\"+?o#\\o%F*F]fr7$$ \"+-BAaXF*$\"+k0SI:F*7%7$$\"+F-=#y%F*Fber7$$\"+v(>y@&F*F]er7$$\"+\"Q$e '3&F*$\"+Wr&*G:F*7%7$$!+)\\!*)4_F*$\"+5hqZp;F*7%7$$!+=FuwYF*$\"+v$F*$\"++ +p8;F*7$$!+z+_#z$F*$\"+3Mwj;F*7%7$$!+DR+3OF*$\"+fHHe#F*$\"+*R&)Qg\"F*7$$!+!='y@AF*$\"+I\\nb;F*7%7$$!+.0!p+#F*$\"+ 4%yiw\"F*7$$!+H+Jx;F*$\"+XE9-;F*7$$!+MgP(p\"F*$\"+/'eTl\"F*7%7$$!+h#)> $[\"F*$\"+XwUl!yq*fFip$\"+%3#G6;F*7$$!+Rc)HO'Fip$ \"+:w$=m\"F*7%7$$!+R+Y!4&Fip$\"+5\\r@$[\"F*F i]t7$$\"+Eu%*f8F*$\"+![+qu\"F*7%7$$\"+C+Jx;F*F^]t7$$\"+)\\+p+#F*Fi\\t7 $$\"+T'\\U)=F*$\"+)\\@su\"F*7%7$$\"+\\PM)>#F*F^\\t7$$\"+`$)\\QDF*Fi[t7 $$\"+;&\\YT#F*$\"+&ehnu\"F*7%7$$\"+O-a;FF*F^[t7$$\"+ZM$H2$F*Fijs7$$\"+ A5OZHF*$\"+\"pZfu\"F*7%7$$\"+S85MKF*F^js7$$\"+AR+3OF*Fiis7$$\"+=,v![$F *$\"+a%4\\u\"F*7%7$$\"+xr*>v$F*F^is7$$\"+l'RF9%F*Fihs7$$\"+0h19SF*$\"+ %*=tVF*7$$!+nY'yF%F*$\"+UbTC=F*7$$!+/iq=VF*$\"+8 vWu=F*7%7$$!+d>wNTF*$\"+qBBo>F*7$$!+()[(*ePF*$\"+;8C@=F*7$$!+wph%z$F*$ \"+m^!>(=F*7%7$$!+eQn,OF*$\"+o1Hr>F*7$$!+39VSKF*$\"+=I===F*7$$!+_lzqKF *$\"+>RRp=F*7%7$$!+1\\znIF*$\"+ln.u>F*7$$!+$yy;s#F*$\"+@pV:=F*7$$!+rE0 ZFF*$\"+,13n=F*7%7$$!+0TGNDF*$\"+`M8w>F*7$$!+0!e:?#F*$\"+L-M8=F*7$$!+W *QHA#F*$\"+/BFl=F*7%7$$!+o%Ql+#F*$\"+J3#p(>F*7$$!+k?nx;F*$\"+bGb7=F*7$ $!+O(3vp\"F*$\"+')Gek=F*7%7$$!+-=m'[\"F*$\"+]:zu>F*7$$!+_r\"\\9\"F*$\" +O@o9=F*7$$!+ZG()o6F*$\"+uSVm=F*7%7$$!+J!))G')*Fip$\"+K?hk>F*7$$!+>deE fFip$\"+a;'[#=F*7$$!+P-5UjFip$\"+5+![(=F*7%7$$!+K:fA^Fip$\"+#[z'G>F*7$ $!*GkcS\"Fip$\"+/Uzg=F*7$$!+4]125Fip$\"+B>S+>F*7%7$$\"*djcS\"FipFjau7$ $\"+t9fA^FipFeau7$$\"+/*4=$QFip$\"+9?*)Q>F*7%7$$\"+\\ceEfFipFj`u7$$\"+ rz)G')*FipFe`u7$$\"+)eLRd)Fip$\"+*pOS&>F*7%7$$\"+Yr\"\\9\"F*Fj_u7$$\"+ 'zhm[\"F*Fe_u7$$\"+F*7%7$$\"+f?nx;F*Fj^u7$$\"+j%Ql+#F* Fe^u7$$\"+0=(R)=F*$\"+Suxd>F*7%7$$\"+-!e:?#F*Fj]u7$$\"+,TGNDF*Fe]u7$$ \"++u:7CF*$\"+#*Rdd>F*7%7$$\"+!yy;s#F*Fj\\u7$$\"+.\\znIF*Fe\\u7$$\"+8h HVHF*$\"+)p/q&>F*7%7$$\"+19VSKF*Fj[u7$$\"+cQn,OF*Fe[u7$$\"+JkhvMF*$\"+ 7S?c>F*7%7$$\"+')[(*ePF*Fjjt7$$\"+c>wNTF*Fejt7$$\"+e/D3SF*$\"+FsCb>F*7 %7$$\"+nY'yF%F*Fjit7$$\"+bP]pYF*Feit7$$\"+#fg2a%F*$\"+#3!>a>F*7%7$$\"+ )[Ytz%F*Fjht7$$\"+9Nl-_F*Feht7$$\"+;?$H2&F*$\"+$[wI&>F*7%7$$!+'[wh>&F* $\"+-^Uv@F*7$$!+:N#Q![F*$\"+;75N?F*7$$!+6#>\\%[F*$\"+x)*4&3#F*7%7$$!+* GAKm%F*$\"+GjGy@F*7$$!+Mh9%G%F*$\"+!**RA.#F*7$$!+\\!z0K%F*$\"+dP\"G3#F *7%7$$!+E@%*HTF*$\"+4B2\"=#F*7$$!+>ZzkPF*$\"+4SXH?F*7$$!+L2Z'z$F*$\"+/ x`!3#F*7%7$$!+U\"zmf$F*$\"+!RaO=#F*7$$!+DhUXKF*$\"+G>(o-#F*7$$!+9,[sKF *$\"+y*y$y?F*7%7$$!+[_5kIF*$\"+*eFe=#F*7$$!+S%o`s#F*$\"+H()pC?F*7$$!+U VN[FF*$\"+\"*4_w?F*7%7$$!+wx]LDF*$\"+bsB(=#F*7$$!+NVL.AF*$\"+j!*GB?F*7 $$!+s^eBAF*$\"+gNHv?F*7%7$$!+M!*Q2?F*$\"+*ptr=#F*7$$!+)\\@on\"F*$\"+>E NB?F*7$$!+#Q(>(p\"F*$\"++$\\`2#F*7%7$$!+ZSu!\\\"F*$\"+EW*Q=#F*7$$!+3\\ $39\"F*$\"+#*=jE?F*7$$!+i8#F*7$$!*k5P;\"Fip$\"+anIu?F*7$$!+10,75Fip$\"+]L'G6#F*7%7$$\"*% *4P;\"FipFbcv7$$\"+OoyY^FipF]cv7$$\"+GB>kQFip$\"+Fr'z9#F*7%7$$\"+\"fM< 'eFipFbbv7$$\"+H!Rx#**FipF]bv7$$\"+kIoH')Fip$\"+@(*[j@F*7%7$$\"+,\\$39 \"F*Fbav7$$\"+TSu!\\\"F*F]av7$$\"+[>%eO\"F*$\"+Y:Mn@F*7%7$$\"+$\\@on\" F*Fb`v7$$\"+H!*Q2?F*F]`v7$$\"+q\\i%)=F*$\"+sPBo@F*7%7$$\"+JVL.AF*Fb_v7 $$\"+rx]LDF*F]_v7$$\"+9$*y5CF*$\"+-,Do@F*7%7$$\"+P%o`s#F*Fb^v7$$\"+X_5 kIF*F]^v7$$\"+1QTSHF*$\"+3!zy;#F*7%7$$\"+BhUXKF*Fb]v7$$\"+R\"zmf$F*F]] v7$$\"+6hjrMF*$\"+UEFn@F*7%7$$\"+=ZzkPF*Fb\\v7$$\"+D@%*HTF*F]\\v7$$\"+ tY].SF*$\"+aL]m@F*7%7$$\"+Mh9%G%F*Fb[v7$$\"+*GAKm%F*F][v7$$\"+9/^NXF*$ \"+w,il@F*7%7$$\"+;N#Q![F*Fbju7$$\"+([wh>&F*F]ju7$$\"+j$yt1&F*$\"+Q&F*$\"+mYU)Q#F*7$$!+fC`4[F*$\"+%GaJC#F*7$$!+I.hY[F*$\"+ )*Hl$H#F*7%7$$!+Ka&yl%F*$\"+8y(4R#F*7$$!+!*H^*G%F*$\"+P6gSAF*7$$!+d(oA K%F*$\"+ldd\"H#F*7%7$$!+C:D#F*7$$!+Nld4jFip$\"+8h[+BF*7 %7$$!+LfQl^Fip$\"+ic@WBF*7$$!)F?x(*Fip$\"+)GjtG#F*7$$!+]*ys,\"Fip$\"+e -,DBF*7%7$$\")e>x(*FipFjdw7$$\"+seQl^FipFedw7$$\"+2;b!*QFip$\"+K[CdBF* 7%7$$\"+.29.eFipFjcw7$$\"+LR\"o)Fip$\"+fZ#HP#F*7% 7$$\"+IUWO6F*$\"+ervQAF*7$$\"+7Z8&\\\"F*$\"+#z@GR#F*7$$\"+Y2Lp8F*$\"+W .SxBF*7%7$$\"+\"*e6v;F*Fjaw7$$\"+JY44?F*Feaw7$$\"+W\"Rf)=F*$\"+\\dhyBF *7%7$$\"+3B+/AF*Fj`w7$$\"+%zRG`#F*Fe`w7$$\"+/lF5CF*$\"+^7$)yBF*7%7$$\" +#ztys#F*Fj_w7$$\"+\"*)*fhIF*Fe_w7$$\"+!>t%QHF*$\"+CmiyBF*7%7$$\"+&4r# \\KF*Fj^w7$$\"+nT$Gf$F*Fe^w7$$\"+]8hoMF*$\"+l2=yBF*7%7$$\"+>`cpPF*Fj]w 7$$\"+B:&F*Fe[w7$$\"+%o&fi]F*$\"+g%>gP#F*7%7$$!+b&)\\&=&F*$\"+G-)4g#F*7$$!+X9 ]9[F*$\"+a8l^CF*7$$!+-%f\"[[F*$\"+f=`-DF*7%7$$!+2BL`YF*$\"+9^B.EF*7$$! +:h.%H%F*$\"+okR\\CF*7$$!+X9vBVF*$\"+A$o1]#F*7%7$$!+A\"H87%F*$\"+$3*H0 EF*7$$!+AxStPF*$\"+*\\KtW#F*7$$!+d.P*z$F*$\"+Q$H*)\\#F*7%7$$!+%ek**e$F *$\"+.M.2EF*7$$!+#oS@D$F*$\"+z\")fXCF*7$$!+&>L[F$F*$\"+D6W(\\#F*7%7$$! +'\\b+1$F*$\"+n]@3EF*7$$!+#>=%HFF*$\"+:lTWCF*7$$!+@i\")\\FF*$\"+2=T'\\ #F*7%7$$!+nI-LDF*$\"+$pX%3EF*7$$!+V!>Q?#F*$\"+*)e=WCF*7$$!+;EwBAF*$\"+ \"Q4i\\#F*7%7$$!+lWR6?F*$\"+_o!pg#F*7$$!+ng\"Gn\"F*$\"+IZsXCF*7$$!+F5v &p\"F*$\"+.1b(\\#F*7%7$$!+/(G'*\\\"F*$\"+8Sj,EF*7$$!+]-&>8\"F*$\"+pv*4 X#F*7$$!+#3\"[k6F*$\"+R_*>]#F*7%7$$!+N:(Q+\"F*$\"+CVN(e#F*7$$!+0%e2v&F ip$\"+esFlCF*7$$!+$[PwH'Fip$\"+.v98DF*7%7$$!+f-&*z^Fip$\"+!QwDb#F*7$$! ),x?$)Fip$\"+-_0+DF*7$$!+ahbA5Fip$\"+$35p`#F*7%7$$\")Kw?$)Fip$\"+._0+D F*7$$\"+)>]*z^Fip$\"+zjd_DF*7$$\"+'QWB\"RFip$\"+C*)omDF*7%7$$\"+O$e2v& FipFfex7$$\"+G:(Q+\"F*Faex7$$\"+QX&)G()Fip$\"+\\OO#e#F*7%7$$\"+W-&>8\" F*Ffdx7$$\"+)pG'*\\\"F*Fadx7$$\"+*3]HP\"F*$\"+*=/ue#F*7%7$$\"+ig\"Gn\" F*Ffcx7$$\"+gWR6?F*Facx7$$\"+t1s()=F*$\"+>)Q*)e#F*7%7$$\"+R!>Q?#F*Ffbx 7$$\"+jI-LDF*Fabx7$$\"+7rT5CF*$\"+.EM*e#F*7%7$$\"+*==%HFF*Ffax7$$\"+$ \\b+1$F*Faax7$$\"+qLGPHF*$\"+1NG*e#F*7%7$$\"+!oS@D$F*Ff`x7$$\"+#ek**e$ F*Fa`x7$$\"+a]PmMF*$\"+ZG(*)e#F*7%7$$\"+@xStPF*Ff_x7$$\"+@\"H87%F*Fa_x 7$$\"+rtj'*RF*$\"+%Q%\\)e#F*7%7$$\"+:h.%H%F*Ff^x7$$\"+2BL`YF*Fa^x7$$\" +ByYFXF*$\"+!)G*ye#F*7%7$$\"+Y9]9[F*Ff]x7$$\"+c&)\\&=&F*Fa]x7$$\"+_+^e ]F*$\"+M%*>(e#F*7%7$$!+K9A\"=&F*$\"+P'oJ\"GF*7$$!+o&y(=[F*$\"+xb^gEF*7 $$!+oca\\[F*$\"+x!)o6FF*7%7$$!+84d\\YF*$\"+W*R^\"GF*7$$!+4vz(H%F*$\"+q UaeEF*7$$!+PD-DVF*$\"+)*o.5FF*7%7$$!+LhH=TF*$\"+%*y(o\"GF*7$$!+62WwPF* $\"+?j!ol#F*7$$!+9AV+QF*$\"+/cb3FF*7%7$$!+$o:ze$F*$\"+<(Q#=GF*7$$!+$e* =aKF*$\"+(\\Xal#F*7$$!+A0dvKF*$\"+ovP2FF*7%7$$!+`yGfIF*$\"+g$))*=GF*7$ $!+Oe=IFF*$\"+aepaEF*7$$!+0r4]FF*$\"+E8s1FF*7%7$$!+)fdQ`#F*$\"+&G.(=GF *7$$!+7X)H?#F*$\"+H4)\\l#F*7$$!++uXBAF*$\"+8:(pq#F*7%7$$!+=o49?F*$\"+6 C^;GF*7$$!+9P6q;F*$\"+.=&Fip$\"+q;BhFF*7$$!)hHhrFip$\"+WDX7FF*7$$!+'*fnF5Fip$\"+ &>8'[FF*7%7$$\")#*GhrFip$\"+XDX7FF*7$$\"+Q\\a\">&Fip$\"+p;BhFF*7$$\"+p BhIRFip$\"+R.FwFF*7%7$$\"+W2@/dFipFbgy7$$\"+)GE&35F*F]gy7$$\"+x\"[@x)F ip$\"+\\@#=z#F*7%7$$\"+vy[F6F*Fbfy7$$\"+o54/:F*F]fy7$$\"+Defw8F*$\"+mY O(z#F*7%7$$\"+4P6q;F*Fbey7$$\"+8o49?F*F]ey7$$\"+Y$G)*)=F*$\"+8L@*z#F*7 %7$$\"+3X)H?#F*Fbdy7$$\"+%fdQ`#F*F]dy7$$\"+L#e5T#F*$\"+4+!)*z#F*7%7$$ \"+Le=IFF*Fbcy7$$\"+]yGfIF*F]cy7$$\"+lPpOHF*$\"+!4t)*z#F*7%7$$\"+#e*=a KF*Fbby7$$\"+\"o:ze$F*F]by7$$\"+!)*)ykMF*$\"+c#z'*z#F*7%7$$\"+52WwPF*F bay7$$\"+KhH=TF*F]ay7$$\"+&*)fU*RF*$\"+`TJ*z#F*7%7$$\"+4vz(H%F*Fb`y7$$ \"+84d\\YF*F]`y7$$\"+*etW_%F*$\"+cY#))z#F*7%7$$\"+p&y(=[F*Fb_y7$$\"+L9 A\"=&F*F]_y7$$\"+qh/b]F*$\"+B/C)z#F*7%7$$!+'zyv<&F*$\"+eF0DIF*7$$!+07U A[F*$\"+)3%opGF*7$$!+qBw][F*$\"+r-3@HF*7%7$$!++z[YYF*$\"+]qvEIF*7$$!+A 0)3I%F*$\"+'zzz'GF*7$$!+B))3EVF*$\"+\\kj>HF*7%7$$!+&*G'f6%F*$\"+j@>GIF *7$$!+\\RxyPF*$\"+$oWl'GF*7$$!+gEE,QF*$\"+O=S=HF*7%7$$!+NTb'e$F*$\"+!f 3#HIF*7$$!+J6bbKF*$\"+c#Gb'GF*7$$!+z_1wKF*$\"+Qi^IF*7$$!+.W9B6F*$\"+YzlvGF*7$$!+>Juh6F*$\"+,S( f#HF*7%7$$!+'y\\E,\"F*$\"+Ze9.IF*7$$!+\"*e(Hm&Fip$\"+**4f\"*GF*7$$!+Uy u!G'Fip$\"+U41QHF*7%7$$!+`B\"4?&Fip$\"+mu7qHF*7$$!)2cCiFip$\"+!Q4Y#HF* 7$$!+ubbK5Fip$\"+ow:gHF*7%7$$\")SbCiFipF^jz7$$\"+!H74?&FipFiiz7$$\"+(G 9h%RFip$\"+Xe'f)HF*7%7$$\"+@e(Hm&FipF^iz7$$\"+!y\\E,\"F*Fihz7$$\"+W!3: \"))Fip$\"+C6J,IF*7%7$$\"+(RWJ7\"F*F^hz7$$\"+XXV3:F*Figz7$$\"+Lx>!Q\"F *$\"+g=H2IF*7%7$$\"+\"p]rm\"F*F^gz7$$\"+J)fq,#F*Fifz7$$\"+Qx:#*=F*$\"+ 5oW4IF*7%7$$\"+EYl,AF*F^fz7$$\"+wu=NDF*Fiez7$$\"+;G37CF*$\"+qQ@5IF*7%7 $$\"+OrKIFF*F^ez7$$\"+Yl9fIF*Fidz7$$\"+i`eOHF*$\"+O4T5IF*7%7$$\"+H6bbK F*F^dz7$$\"+LTb'e$F*Ficz7$$\"+w(RPY$F*$\"+34K5IF*7%7$$\"+[RxyPF*F^cz7$ $\"+%*G'f6%F*Fibz7$$\"+3XW#*RF*$\"+/R05IF*7%7$$\"+A0)3I%F*F^bz7$$\"++z [YYF*Fiaz7$$\"+;Q/AXF*$\"+N6m4IF*7%7$$\"+17UA[F*F^az7$$\"+(zyv<&F*Fi`z 7$$\"+9A8_]F*$\"+MB<4IF*7%7$$!+A1^u^F*$\"+$p$oOKF*7$$!+y$*[D[F*$\"+&y0 \"zIF*7$$!+)f6=&[F*$\"+lMnIJF*7%7$$!+*z.Sk%F*$\"+'oP\"QKF*7$$!+BYO.VF* $\"+#z^w2$F*7$$!+EL'pK%F*$\"+m*H%HJF*7%7$$!+s9B9TF*$\"+\\8HRKF*7$$!+s` ]!y$F*$\"+H\")\\wIF*7$$!+6j)=!QF*$\"++-VGJF*7%7$$!+Ynw&e$F*$\"+u'))*RK F*7$$!+?&QjD$F*$\"+/3!e2$F*7$$!+9JNwKF*$\"+K*>y7$F*7%7$$!+L\"4&fIF*$\" +$**p*RKF*7$$!+bX'*HFF*$\"+&[>e2$F*7$$!+;g,]FF*$\"+Tj$y7$F*7%7$$!+M1*o `#F*$\"+P,wQKF*7$$!+w9&**>#F*$\"+T$Hq2$F*7$$!+q+OAAF*$\"+V?*)GJF*7%7$$ !+s!y,-#F*$\"+HzRNKF*7$$!+gC.k;F*$\"+\\:R!3$F*7$$!+`2q#p\"F*$\"+&pe<8$ F*7%7$$!+$f/E^\"F*$\"+G*pxA$F*7$$!+hV(*=6F*$\"+]&>!)3$F*7$$!+8e_g6F*$ \"+1z&z8$F*7%7$$!+\"[)H;5F*$\"+z_E6KF*7$$!+U*)[EcFip$\"+*>CX5$F*7$$!+N K5viFip$\"++oJ]JF*7%7$$!+#3!e3_Fip$\"+X;AzJF*7$$!)yydaFip$\"+LycOJF*7$ $!+E*er.\"Fip$\"+lEdrJF*7%7$$\")5ydaFip$\"+MycOJF*7$$\"+?+e3_Fip$\"+W; AzJF*7$$\"+]ETfRFip$\"+Mov&>$F*7%7$$\"+s))[EcFip$\"++U_/JF*7$$\"+v%)H; 5F*$\"+y_E6KF*7$$\"+5(Qs%))Fip$\"+Ow$3@$F*7%7$$\"+bV(*=6F*Ffi[l7$$\"+( e/E^\"F*Fai[l7$$\"+\\\"4PQ\"F*$\"+&f%>KF*7%7$$\"+s9&**>#F*Ffg[l7$$\"+I1*o`# F*Fag[l7$$\"+*G+MT#F*$\"+]8f?KF*7%7$$\"+_X'*HFF*Fff[l7$$\"+I\"4&fIF*Fa f[l7$$\"+-O'o$HF*$\"+&f24A$F*7%7$$\"+=&QjD$F*Ffe[l7$$\"+Wnw&e$F*Fae[l7 $$\"+KZ8jMF*$\"+pB\"4A$F*7%7$$\"+s`]!y$F*Ffd[l7$$\"+r9B9TF*Fad[l7$$\"+ qZ5\"*RF*$\"+))=t?KF*7%7$$\"+BYO.VF*Ffc[l7$$\"+*z.Sk%F*Fac[l7$$\"+795? XF*$\"+IMU?KF*7%7$$\"+z$*[D[F*Ffb[l7$$\"+B1^u^F*Fab[l7$$\"+6Aq\\]F*$\" +P\"=+A$F*7%7$$!+P\"e><&F*$\"+**G5[MF*7$$!+j=/G[F*$\"+6#R()G$F*7$$!+o2 q_[F*$\"+v#Q/M$F*7%7$$!+?b/UYF*$\"+BDK\\MF*7$$!+-HK0VF*$\"+(e>vG$F*7$$ !+q?mFVF*$\"+\"3(QRLF*7%7$$!+7g,8TF*$\"+>R@]MF*7$$!+K3s\"y$F*$\"+\">Gm G$F*7$$!+-yK-QF*$\"+*H5'QLF*7%7$$!+9\"eae$F*$\"+;Rh]MF*7$$!+_rkcKF*$\" +%>GiG$F*7$$!+viYwKF*$\"+&Hf#QLF*7%7$$!+neFgIF*$\"+z!\\-X$F*7$$!+@y>HF F*$\"+JIf'G$F*7$$!+0et\\FF*$\"+2&z&QLF*7%7$$!+;5()QDF*$\"+(p>'[MF*7$$! +%4rz>#F*$\"+8CA)G$F*7$$!+TRl@AF*$\"+SW**RLF*7%7$$!+IIPB?F*$\"+!)*HZW$ F*7$$!+-v$3m\"F*$\"+I@6#H$F*7$$!+ocj\"p\"F*$\"+S;GVLF*7%7$$!+`#pl^\"F* $\"+zvYOMF*7$$!+,(4]6\"F*$\"+JXP+LF*7$$!+;3Uf6F*$\"+=v\"*\\LF*7%7$$!+K w_>5F*$\"+BB`>MF*7$$!+Nu>%f&Fip$\"+(y4tJ$F*7$$!+6[\"4F'Fip$\"+4qWiLF*7 %7$$!+#fI\\@&Fip$\"+`5[)Q$F*7$$!)otA[Fip$\"+d5O[LF*7$$!+SkZT5Fip$\"+23 )GQ$F*7%7$$\"),tA[FipFf]]l7$$\"+H0$\\@&FipFa]]l7$$\"+\"[J4(RFip$\"+N$G cS$F*7%7$$\"+mt>%f&Fip$\"+)y4tJ$F*7$$\"+Dw_>5F*$\"+AB`>MF*7$$\"+H!o'z) )Fip$\"+*)eS?MF*7%7$$\"+&p4]6\"F*Ff[]l7$$\"+Z#pl^\"F*Fa[]l7$$\"+w**4(Q \"F*$\"+Z03FMF*7%7$$\"+(\\P3m\"F*Ffj\\l7$$\"+DIPB?F*Faj\\l7$$\"+.()=(* =F*$\"+BS\")HMF*7%7$$\"+!4rz>#F*Ffi\\l7$$\"+75()QDF*Fai\\l7$$\"+j)R\\T #F*$\"+iw$4V$F*7%7$$\"+=y>HFF*Ffh\\l7$$\"+keFgIF*Fah\\l7$$\"+]GXPHF*$ \"+2/PJMF*7%7$$\"+]rkcKF*Ffg\\l7$$\"+7\"eae$F*Fag\\l7$$\"+7z*GY$F*$\"+ 6RYJMF*7%7$$\"+K3s\"y$F*Fff\\l7$$\"+6g,8TF*Faf\\l7$$\"+hz;!*RF*$\"+H8O JMF*7%7$$\"+-HK0VF*Ffe\\l7$$\"+?b/UYF*Fae\\l7$$\"+<&z&=XF*$\"+\"HF6V$F *7%7$$\"+k=/G[F*Ffd\\l7$$\"+Q\"e><&F*Fad\\l7$$\"+GppZ]F*$\"+iazIMF*7%7 $$!+Rf')p^F*$\"+GSMfOF*7$$!+hS8I[F*$\"+92b)\\$F*7$$!+g-W`[F*$\"+#3].b$ F*7%7$$!+hsaSYF*$\"+\")RMgOF*7$$!+i6#oI%F*$\"+h2b(\\$F*7$$!+,@?GVF*$\" +KG[\\NF*7%7$$!+[?C7TF*$\"+d+*4m$F*7$$!+'z%\\#y$F*$\"+&o/p\\$F*7$$!+\" \\5E!QF*$\"+tv\"*[NF*7%7$$!+g![be$F*$\"+L96hOF*7$$!+1sbcKF*$\"+4Ly'\\$ F*7$$!+wKVwKF*$\"+M4\")[NF*7%7$$!+=`OhIF*$\"+J3UgOF*7$$!+q$3\"GFF*$\"+ 6RZ(\\$F*7$$!+.(R$\\FF*$\"+,eT\\NF*7%7$$!+NF0TDF*$\"+^eReOF*7$$!+v$*y& >#F*$\"+\"*))\\*\\$F*7$$!+&y&)3A#F*$\"+gU;^NF*7%7$$!+zjeE?F*$\"+eS,aOF *7$$!+`Tid;F*$\"+%o!)Q]$F*7$$!+R,f!p\"F*$\"+CO$[b$F*7%7$$!+u@J?:F*$\"+ &Q'=XOF*7$$!+!ym76\"F*$\"+d$3F^$F*7$$!+A$G%e6F*$\"+hH%=c$F*7%7$$!+o&)Q A5F*$\"+M;%zi$F*7$$!+q!)elbFip$\"+3J&*HNF*7$$!+Y\\#zE'Fip$\"+M(fWd$F*7 %7$$!+#zX-A&Fip$\"+H$zyf$F*7$$!)o@\"H%Fip$\"+8a,gNF*7$$!+UI^X5Fip$\"+f )*4%f$F*7%7$$\"),@\"H%FipFb_^l7$$\"+HdC?_FipF]_^l7$$\"+$Q&*4)RFip$\"+> #obh$F*7%7$$\"+,!)elbFip$\"+4J&*HNF*7$$\"+i&)QA5F*$\"+L;%zi$F*7$$\"+i/ 74*)Fip$\"+$)z,IOF*7%7$$\"+tnE66F*Fb]^l7$$\"+p@J?:F*F]]^l7$$\"+f=N!R\" F*$\"+?j&pj$F*7%7$$\"+[Tid;F*Fb\\^l7$$\"+ujeE?F*F]\\^l7$$\"+Iqy**=F*$ \"+Tt&*ROF*7%7$$\"+r$*y&>#F*Fb[^l7$$\"+JF0TDF*F][^l7$$\"+@dk;CF*$\"+=o DTOF*7%7$$\"+n$3\"GFF*Fbj]l7$$\"+:`OhIF*F]j]l7$$\"+d@HQHF*$\"+NY!=k$F* 7%7$$\"+/sbcKF*Fbi]l7$$\"+e![be$F*F]i]l7$$\"+5p'HY$F*$\"+$*G)>k$F*7%7$ $\"+&z%\\#y$F*Fbh]l7$$\"+Z?C7TF*F]h]l7$$\"+%*Hd*)RF*$\"+%*=&>k$F*7%7$$ \"+i6#oI%F*Fbg]l7$$\"+hsaSYF*F]g]l7$$\"+g0Uxq$F*7$$!+I.gGVF*$\"+LmpfPF*7%7$$! +[`%=6%F*$\"+vOkrQF*7$$!+'\\\"*Gy$F*$\"+*p.tq$F*7$$!+_ev-QF*$\"+S?LfPF *7%7$$!+@#pfe$F*$\"+dD]rQF*7$$!+Xg8cKF*$\"+<[W2PF*7$$!+z*yiF$F*$\"+=gX fPF*7%7$$!++3riIF*$\"+\")Q]qQF*7$$!+))GwEFF*$\"+$\\V%3PF*7$$!+tQ&)[FF* $\"+#*zKgPF*7%7$$!+DcPVDF*$\"+a\\5oQF*7$$!+'[mM>#F*$\"+?C%3r$F*7$$!+& \\z+A#F*$\"+9iQiPF*7%7$$!+O]xH?F*$\"+!*[EjQF*7$$!+(\\NWl\"F*$\"+%[#o:P F*7$$!+*Qz&*o\"F*$\"+*)>SmPF*7%7$$!+!oFQ_\"F*$\"+Qs$R&QF*7$$!+u7v26F*$ \"+O,,DPF*7$$!+RZad6F*$\"+$\\FPx$F*7%7$$!+mv#\\-\"F*$\"+4h[OQF*7$$!+#4 )>SbFip$\"+l7YUPF*7$$!+cc\"fE'Fip$\"+HOO'y$F*7%7$$!+EotC_Fip$\"++`R2QF *7$$!)M6UQFip$\"+u?brPF*7$$!+O8G\\5Fip$\"+RRC0QF*7%7$$\")m5UQFipF^a_l7 $$\"+kntC_FipFi`_l7$$\"+(Rc)*)RFip$\"+#fmb#QF*7%7$$\"+C!)>SbFipF^`_l7$ $\"+gv#\\-\"F*Fi__l7$$\"+kF!f$*)Fip$\"+@XnRQF*7%7$$\"+o7v26F*F^__l7$$ \"+vw#Q_\"F*Fi^_l7$$\"+rZX$R\"F*$\"+Av#o%QF*7%7$$\"+\"\\NWl\"F*F^^_l7$ $\"+J]xH?F*Fi]_l7$$\"+N@R->F*$\"+R$z+&QF*7%7$$\"+\"[mM>#F*F^]_l7$$\"+@ cPVDF*Fi\\_l7$$\"+GNZ=CF*$\"+u?b^QF*7%7$$\"+&)GwEFF*F^\\_l7$$\"+(z5F1$ F*Fi[_l7$$\"+p?LRHF*$\"+tT@_QF*7%7$$\"+Vg8cKF*F^[_l7$$\"+>#pfe$F*Fij^l 7$$\"+)>!HjMF*$\"+tYZ_QF*7%7$$\"+&\\\"*Gy$F*F^j^l7$$\"+Z`%=6%F*Fii^l7$ $\"+1&o#*)RF*$\"+>2^_QF*7%7$$\"+$)y\"zI%F*F^i^l7$$\"+R0XRYF*Fih^l7$$\" +N^d;XF*$\"+2SS_QF*7%7$$\"+$*p\"=$[F*F^h^l7$$\"+4I=o^F*Fig^l7$$\"+SrvW ]F*$\"+Cd>_QF*7%7$$!+]I'o;&F*$\"+8mR\"3%F*7$$!+^p8L[F*$\"+$R.'=RF*7$$! +!*y^a[F*$\"+ka`qRF*7%7$$!+#y.(QYF*$\"+Hd*>3%F*7$$!+SYm3VF*$\"+xU+=RF* 7$$!+#)G()GVF*$\"+D9,qRF*7%7$$!+[1x6TF*$\"+1R>#3%F*7$$!+'>mHy$F*$\"++h !y\"RF*7$$!+fKy-QF*$\"+Ft$)pRF*7%7$$!+M\\m'e$F*$\"+*H/=3%F*7$$!+K.WbKF *$\"+2d>=RF*7$$!+x[-wKF*$\"+P#z,(RF*7%7$$!+?vDkIF*$\"+vJ^!3%F*7$$!+oh@ DFF*$\"+Jo[>RF*7$$!+U+I[FF*$\"+D@IrRF*7%7$$!+#)=zXDF*$\"+>.wxSF*7$$!+G -0\">#F*$\"+(oRA#RF*7$$!+^QD>AF*$\"+uzktRF*7%7$$!+>v!H.#F*$\"+.X\\sSF* 7$$!+9II^;F*$\"+.b]FRF*7$$!+^Ph)o\"F*$\"+nn(z(RF*7%7$$!+.t6F:F*$\"+]\" GF1%F*7$$!+^;Y/6F*$\"+c=FPRF*7$$!+#>kn:\"F*$\"+Bnc&)RF*7%7$$!+&e&=F5F* $\"+Px:XSF*7$$!+'*yhF*$\"+*o$=gSF*7 %7$$\"+C-0\">#F*Ff^`l7$$\"+y=zXDF*Fa^`l7$$\"+fyQ?CF*$\"+(>E=1%F*7%7$$ \"+lh@DFF*Ff]`l7$$\"+mHy$F *Ff[`l7$$\"+Z1x6TF*Fa[`l7$$\"+07@*)RF*$\"+DJ/jSF*7%7$$\"+SYm3VF*Ffj_l7 $$\"+#y.(QYF*Faj_l7$$\"+$)3+;XF*$\"+&\\#*H1%F*7%7$$\"+_p8L[F*Ffi_l7$$ \"+^I'o;&F*Fai_l7$$\"+]jtV]F*$\"+_r$G1%F*-%&COLORG6&%$RGBG$\"\"(!\"\"$ \"#&)!\"#$\"#vFb[al-%+AXESLABELSG6$%\"xG%%y(x)G-%%VIEWG6$;$!+++++bF*$ \"+++++bF*;$!+++++?Fip$\"+++++UF*" 2 538 385 385 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 3374 -13232 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "soln_curve1 := plot(subs(C=1,exp(1/2*LambertW(exp(-2*C)*x^2)+C)),x =-5..5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "soln_curve2 := \+ plot(subs(C=-10,exp(1/2*LambertW(exp(-2*C)*x^2)+C)),x=-5..5):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "display(\{direction_field_pl ot,soln_curve1,soln_curve2\});" }}{PARA 13 "" 1 "" {INLPLOT "6'-%'CURV ESG6$7V7$$!\"&\"\"!$\"+%4<2u%!\"*7$$!+e%G?y%F-$\"+iE$=j%F-7$$!+'esBf%F -$\"+g%Hq`%F-7$$!+@Z3zVF-$\"+X!)QIWF-7$$!+YIQkTF-$\"+9?2BVF-7$$!+6=q]R F-$\"+**QP;UF-7$$!+_>f_PF-$\"+u'Gw6%F-7$$!+p1YZNF-$\"+JVm:SF-7$$!+-OJN LF-$\"+Nfk5RF-7$$!+%*o%Q7$F-$\"+@Md1QF-7$$!+#RFj!HF-$\"+>LQ+PF-7$$!+'4 OZr#F-$\"+8\\!yg$F-7$$!+v'\\!*\\#F-$\"+l(y\\]$F-7$$!+DwZ#G#F-$\"+aUl.M F-7$$!+D.xt?F-$\"+6'o$3LF-7$$!+.TC%)=F-$\"+jSRCKF-7$$!+#4z)e;F-$\"+(=n &GJF-7$$!+n`'zY\"F-$\"+pFp^IF-7$$!+>t)eC\"F-$\"+'RY&oHF-7$$!+<1J\\5F-$ \"+\"[C>!HF-7$$!*>[jL)F-$\"+e*4\"QGF-7$$!*d/EG'F-$\"+-S<)y#F-7$$!*bQ(R TF-$\"+WIF\\FF-7$$!*h=><#F-$\"+2v\"ps#F-7$$!+!zQ16\"!#5$\"+Dza?FF-7$$! ((*e$\\F-$\"+6jG=FF-7$$\"++D,`5F^s$\"+E\">.s#F-7$$\"*(RQb@F-$\"+MryEFF -7$$\"+v:+:JF^s$\"+%Gdft#F-7$$\"*=>Y2%F-$\"+&H@$[FF-7$$\"*yXu9'F-$\"+6 DI&y#F-7$$\"*\\y))G)F-$\"+8#Ho$GF-7$$\"+i_QQ5F-$\"+tJW)*GF-7$$\"+!y%3T 7F-$\"+EY$o'HF-7$$\"+O![hY\"F-$\"+oI)40$F-7$$\"+#Qx$o;F-$\"+-K]KJF-7$$ \"+u.I%)=F-$\"+u&=WA$F-7$$\"+(pe*z?F-$\"+[Z:6LF-7$$\"+C\\'QH#F-$\"+t^# *3MF-7$$\"+8S8&\\#F-$\"+i\"GJ]$F-7$$\"+0#=bq#F-$\"+>wP.OF-7$$\"+2s?6HF -$\"+HSv-PF-7$$\"+IXaEJF-$\"+yj*y!QF-7$$\"+l*RRL$F-$\"+Nx'*4RF-7$$\"+` <.YNF-$\"+O`&\\,%F-7$$\"+8tOcPF-$\"+)H3&>TF-7$$\"+\\Qk\\RF-$\"+Qg%e@%F -7$$\"+p0;rTF-$\"+h%ekK%F-7$$\"+lxGpVF-$\"+N**[DWF-7$$\"+!oK0e%F-$\"+) *)46`%F-7$$\"+<5s#y%F-$\"+l(y@j%F-7$$\"\"&F*F+-%'COLOURG6&%$RGBG$\"#5! \"\"F*F*-F$6]dl7%7$$!+&*y:j_F-F*7$$!+0@%ot%F-F*7$$!+;Gz][F-$\"+[*y:j#! #67%7$$!+1@%ot%F-F*7$$!+;j_5UF-F*7$$!+FqZCVF-Fi\\l7%7$$!+AF-Fi\\l7%7$$!+hJE0@F-F*7$$!+rt%*y:F-F* 7$$!+#3)*Gp\"F-Fi\\l7%7$$!+st%*y:F-F*7$$!+#eJE0\"F-F*7$$!+$H#em6F-Fi\\ l7%F\\al7$$!+Fz:j_F^sF*7$$!+Q]m-kF^sFi\\l7%7$$!+Gz:j_F^sF*7$$!#KF^sF*7 $$!+Vr]R6F^sFi\\l7%7$$!#LF^sF*7$$\"+jy:j_F^sF*7$$\"+_2lBTF^sFi\\l7%7$$ \"+iy:j_F^sF*7$$\"+w:j_5F-F*7$$\"+\\'3oQ*F^sFi\\l7%Facl7$$\"+mt%*y:F-F *7$$\"+bm*\\Y\"F-Fi\\l7%Fhcl7$$\"+cJE0@F-F*7$$\"+XCJ\"*>F-Fi\\l7%F_dl7 $$\"+Y*y:j#F-F*7$$\"+N#Gw^#F-Fi\\l7%Ffdl7$$\"+OZ*y:$F-F*7$$\"+DS%R/$F- Fi\\l7%F]el7$$\"+E0@%o$F-F*7$$\"+:)f-d$F-Fi\\l7%Fdel7$$\"+;j_5UF-F*7$$ \"+0cd'4%F-Fi\\l7%F[fl7$$\"+1@%ot%F-F*7$$\"+&R\"*Gi%F-Fi\\l7%Fbfl7$$\" +'*y:j_F-F*7$$\"+&=2#\\^F-Fi\\l7%7$$!+Lqrh_F-$\"+(yk_@#F^s7$$!+nHGQZF- $\"+H:E&*>F^s7$$!+lYtW[F-$\"+k1h/BF^s7%7$$!+4v/NZF-$\"+ye)zA#F^s7$$!+8 4K7UF-$\"+Q/a#)>F^s7$$!+rV#yJ%F-$\"+KU/(H#F^s7%7$$!+w2B3UF-$\"+J^*RC#F ^s7$$!+og]'o$F-$\"+&=Jl'>F^s7$$!+K?z!z$F-$\"+XiY(G#F^s7%7$$!+(4t6o$F-$ \"+zLtkAF^s7$$!+p@$4;$F-$\"+QHzX>F^s7$$!+X2gjKF-$\"+Lg'\\F#F^s7%7$$!+n Mp`JF-$\"+_Vg#H#F^s7$$!+@-yNEF-$\"+l>#z\">F^s7$$!+.H?OFF-$\"+/(**zD#F^ s7%7$$!+PoSDEF-$\"+>U!>L#F^s7$$!+u_V6@F-$\"+(4A'y=F^s7$$!+:$[&3AF-$\"+ PjuLAF^s7%7$$!+kGQ&4#F-$\"+58*4R#F^s7$$!+ow#))e\"F-$\"+1]`>=F^s7$$!+w? k!o\"F-$\"+Bl`'>#F^s7%7$$!+M/'4c\"F-$\"+\\^u([#F^s7$$!+?&=12\"F-$\"+n6 yAH F^s7$$!*#[[H'*F^s$\"+kqH\"H\"F^s7$$!+tyvw6F^s$\"+sxh5=F^s7%7$$\"*A%[H' *F^s$\"+iqH\"H\"F^s7$$\"+3%4-I%F^s$\"+a#H#>HF^s7$$\"+*RU*oIF^s$\"+XYjL FF^s7%7$$\"+j@cgcF^s$\"+.r.\\:F^s7$$\"+Y6*G,\"F-$\"+8#*[hEF^s7$$\"+vT% Q\"))F^s$\"+JP0WEF^s7%7$$\"+:&=12\"F-$\"+m6yAF-$\"+*)\\a?DF^s7%7$$\"+q_V6@F-$\"+'4A'y=F^s7 $$\"+LoSDEF-$\"+?U!>L#F^s7$$\"+fO'**\\#F-$\"+V:v!\\#F^s7%7$$\"+=-yNEF- $\"+k>#z\">F^s7$$\"+kMp`JF-Fc[m7$$\"+LJ&)HIF-$\"+e)R/Z#F^s7%7$$\"+n@$4 ;$F-$\"+PHzX>F^s7$$\"+&4t6o$F-Fcjl7$$\"+T2deNF-$\"+77!eX#F^s7%7$$\"+ng ]'o$F-Fhil7$$\"+v2B3UF-Fcil7$$\"+9Lg'3%F-$\"+yZyWCF^s7%7$$\"+84K7UF-Fh hl7$$\"+4v/NZF-Fchl7$$\"+6P?9YF-$\"+z'3iV#F^s7%7$$\"+oHGQZF-Fhgl7$$\"+ Mqrh_F-Fcgl7$$\"+L^^T^F-$\"+<(\\$HCF^s7%7$$!+@)*ed_F-$\"+Qm\"fU%F^s7$$ !+!=5Cu%F-$\"+%*f8&*RF^s7$$!+\\z[S[F-$\"+gD*fM%F^s7%7$$!+xT'*HZF-$\"+G Jh\\WF^s7$$!+XUSCGJ%F^s7 %7$$!+Ai*Gn$F-$\"+YC'e^%F^s7$$!+X!4#pJF-$\"+'=!>0RF^s7$$!+5q[#*G%F^s7%7$$!+l_kUJF-$\"+]$\\Oc%F^s7$$!+B%Gok#F-$\"+#G.u&QF^s7$$!+Hd 5KFF-$\"+i%=#eUF^s7%7$$!+7M55EF-$\"+j0-FYF^s7$$!+*pQn7#F-$\"+p?.%z$F^s 7$$!+R$f`?#F-$\"+D<1;UF^s7%7$$!+RJOt?F-$\"+-3(Gr%F^s7$$!+$RZ3h\"F-$\"+ I==3PF^s7$$!+f%)ez;F-$\"+Y7'p:%F^s7%7$$!+e]xG:F-$\"+K=xG[F^s7$$!+'*Q!G 5\"F-$\"++3G#f$F^s7$$!+8!*Qc6F-$\"+UX(H2%F^s7%7$$!+7RZ?(*F^s$\"+yh o\\F^s7$$\"+G$*4c%)F^s$\"+s#GH#[F^s7%7$$\"+!*Q!G5\"F-$\"+)z!G#f$F^s7$$ \"+_]xG:F-$\"+M=xG[F^s7$$\"+X#4zR\"F-$\"+_#\\Sx%F^s7%7$$\"+*QZ3h\"F-$ \"+H==3PF^s7$$\"+MJOt?F-$\"+.3(Gr%F^s7$$\"+2!H=%>F-$\"+KrgEZF^s7%7$$\" +&pQn7#F-$\"+o?.%z$F^s7$$\"+2M55EF-$\"+k0-FYF^s7$$\"+')4UzCF-$\"+@cN)o %F^s7%7$$\"+?%Gok#F-Ff^n7$$\"+i_kUJF-Fa^n7$$\"+xvA8IF-$\"+75leYF^s7%7$ $\"+V!4#pJF-Ff]n7$$\"+?i*Gn$F-Fa]n7$$\"+R7wWNF-$\"+7;\\NYF^s7%7$$\"++m'F^s7$$!+T_*\\A%F-$\"+K*f:(fF^s7$$!+yj;6VF-$\"+nYIpjF^s7%7$$ !+z$RD>%F-$\"+m9F)p'F^s7$$!+mu>-PF-$\"+$[2L$fF^s7$$!+![aWy$F-$\"++!)4W jF^s7%7$$!+:7OhOF-$\"+BP\"[u'F^s7$$!+^Su!=$F-$\"+E_w')eF^s7$$!+/n)zD$F -$\"+dn%GJ'F^s7%7$$!+-5:GJF-$\"+@b\">!oF^s7$$!+'oA8m#F-$\"+FMmHeF^s7$$ !+.6,KFF-$\"+QjdtiF^s7%7$$!+?&Q=f#F-$\"+Gb,soF^s7$$!+!f.]9#F-$\"+@Mcfd F^s7$$!+i?)p?#F-$\"+KQ$QA'F^s7%7$$!+Fr\"40#F-$\"+H-TcpF^s7$$!+1MHL;F-$ \"+>(o^n&F^s7$$!+(zsOo\"F-$\"+.vPhhF^s7%7$$!+8I=/:F-$\"+[Zu]qF^s7$$!+U fRF6F-$\"++U$3e&F^s7$$!+J!QI;\"F-$\"+/FZ(3'F^s7%7$$!+rtOj&*F^s$\"+pbvH rF^s7$$!+zj5EiF^s$\"+zL#=]&F^s7$$!+pd\"*RkF^s$\"+(3W6-'F^s7%7$$!+J,t*f %F^s$\"+o8a9qF^s7$$!*HyUj'F^s$\"+!ePqh&F^s7$$!+VB%*y5F^s$\"+T6U;hF^s7% 7$$\"*]xUj'F^s$\"+(ePqh&F^s7$$\"+!3I(*f%F^s$\"+h8a9qF^s7$$\"+(pv2J$F^s $\"+N!)y3pF^s7%7$$\"+:j5EiF^sFbeo7$$\"+0tOj&*F^s$\"+qbvHrF^s7$$\"+'H+@ L)F^s$\"+h4;WpF^s7%7$$\"+OfRF6F-$\"+*>M3e&F^s7$$\"+1I=/:F-$\"+\\Zu]qF^ s7$$\"+3:nw8F-$\"+:L*3#pF^s7%7$$\"+,MHL;F-$\"+=(o^n&F^s7$$\"+@r\"40#F- $\"+I-TcpF^s7$$\"+O,Y?>F-$\"+m^#y)oF^s7%7$$\"+'e.]9#F-$\"+?McfdF^s7$$ \"+;&Q=f#F-F]bo7$$\"+(yJ.Y#F-$\"+Y+eaoF^s7%7$$\"+$oA8m#F-Fbao7$$\"+**4 :GJF-F]ao7$$\"+Eop'*HF-$\"+E4$[#oF^s7%7$$\"+\\Su!=$F-$\"+D_w')eF^s7$$ \"+87OhOF-F]`o7$$\"+H0\\INF-$\"+c$\\$*z'F^s7%7$$\"+lu>-PF-Fb_o7$$\"+y$ RD>%F-F]_o7$$\"+:@ZiSF-$\"+iG#yx'F^s7%7$$\"+T_*\\A%F-Fb^o7$$\"+\"=tBs% F-F]^o7$$\"+_L<$f%F-$\"+AAlfnF^s7%7$$\"+q=q[ZF-Fb]o7$$\"+K\")H^_F-F]]o 7$$\"+-^&H7&F-$\"+k$RUu'F^s7%7$$!+,``V_F-$\"+zO!*>))F^s7$$!+*pkkv%F-$ \"+&e,A-)F^s7$$!+(Q!*p$[F-$\"+bWWQ%)F^s7%7$$!+?)fKr%F-$\"+Akec))F^s7$$ !+-'3TB%F-$\"+U)=b)zF^s7$$!+Aqi5VF-$\"+9ho8%)F^s7%7$$!+twy\"=%F-$\"+>z P**))F^s7$$!+r\"\\Hr$F-$\"+YtsUzF^s7$$!+a.c%y$F-$\"+@vE%Q)F^s7%7$$!+I* p'[OF-$\"+4?L\\*)F^s7$$!+O`V$>$F-$\"+bKx#*yF^s7$$!+c!z*eKF-$\"+KA9\\$) F^s7%7$$!+:sI8JF-$\"+Q=;#F-$\"+*or*oxF^s7$$!+Oh `5AF-$\"+&)Q\"zD)F^s7%7$$!+M@ML?F-$\"+-I;W\"*F^s7$$!+)Ro3l\"F-$\"+iA%z p(F^s7$$!+$*>[)o\"F-$\"+0^H-#)F^s7%7$$!+x,v*[\"F-$\"+\\b)3@*F^s7$$!+x( G=9\"F-$\"+:(>7j(F^s7$$!+79zn6F-$\"+,\")=Z\")F^s7%7$$!+(*pvS&*F^s$\"+` ;NU#*F^s7$$!+`nr[iF^s$\"+6Ov*f(F^s7$$!+&[_\"[kF^s$\"+J&))*>\")F^s7%7$$ !+WubvZF^s$\"+mzVJ!*F^s7$$!*;0g([F^s$\"+)Hn1\"yF^s7$$!+!fzW.\"F^s$\"+Z (p$*G)F^s7%7$$\"*O/g([F^s$\"+1tm5yF^s7$$\"+%Rdbx%F^s$\"+ezVJ!*F^s7$$\" +^mplMF^s$\"+27`\")*)F^s7%7$$\"+)o;([iF^sF\\hp7$$\"+KpvS&*F^sFggp7$$\" +Bup9$)F^s$\"+d2K^!*F^s7%7$$\"+r(G=9\"F-$\"+9(>7j(F^s7$$\"+r,v*[\"F-$ \"+]b)3@*F^s7$$\"+@%e]O\"F-$\"+k&QG/*F^s7%7$$\"+$Ro3l\"F-$\"+hA%zp(F^s 7$$\"+H@ML?F-$\"+.I;W\"*F^s7$$\"+Q(R`!>F-$\"+&*QGA!*F^s7%7$$\"+'=Q=;#F -F\\ep7$$\"+;R+vDF-Fgdp7$$\"+_ezWCF-$\"+4rN(**)F^s7%7$$\"+qk;wEF-$\"+Z I#[$yF^s7$$\"+7sI8JF-Fgcp7$$\"+;T-#)HF-$\"+Kx+s*)F^s7%7$$\"+M`V$>$F-F \\cp7$$\"+G*p'[OF-Fgbp7$$\"+'G\"4[*)F^s7%7$$\"+q\"\\Hr$F-$ \"+XtsUzF^s7$$\"+swy\"=%F-Fgap7$$\"+HeQ]SF-$\"+XinE*)F^s7%7$$\"+-'3TB% F-F\\ap7$$\"+?)fKr%F-Fg`p7$$\"+w'*H#e%F-$\"+o.d2*)F^s7%7$$\"++ZYcZF-F \\`p7$$\"+-``V_F-Fg_p7$$\"+LK:8^F-$\"+59t!*))F^s7%7$$!+#Q+]B&F-$\"+hc+ +6F-7$$!+='**\\w%F-$\"+(\\d_+\"F-7$$!+n*[r$[F-$\"+:6F\\5F-7%7$$!+Hwa.Z F-$\"+<)zQ5\"F-7$$!+$z?QC%F-$\"+TLQ,5F-7$$!+CWK6VF-$\"+@3cY5F-7%7$$!+( )eyqTF-$\"+%=a#36F-7$$!+d4&Rs$F-$\"+O(*3q**F^s7$$!+H%Hfy$F-$\"+:gVV5F- 7%7$$!+PiOOOF-$\"+g@:86F-7$$!+H!Rd?$F-$\"+$)*46#**F^s7$$!+#>Z6E$F-$\"+ R&[)R5F-7%7$$!+dg$**4$F-$\"+w\\`=6F-7$$!+Jw`*o#F-$\"+A=Gn)*F^s7$$!+u=? PFF-$\"+6^yN5F-7%7$$!+mALhDF-$\"+#\\FU7\"F-7$$!+W)4b<#F-$\"+emN5)*F^s7 $$!+.aH9AF-$\"+F(G8.\"F-7%7$$!+X8<@?F-$\"+OxwH6F-7$$!+(=RIm\"F-$\"+?U& \\v*F^s7$$!+wpO#p\"F-$\"+mH!o-\"F-7%7$$!+FDl#[\"F-$\"+*=GS8\"F-7$$!+Fk #*[6F-$\"+&p\\Br*F^s7$$!+mtIq6F-$\"+Sq;B5F-7%7$$!+iEVz&*F^s$\"+xp\\L6F -7$$!+)3T+@'F^s$\"+6=m<(*F^s7$$!+Eq7MkF^s$\"+$))GO-\"F-7%7$$!+2p#)**[F ^s$\"+>@+16F-7$$!*`5Lj$F^s$\"+*Q5E***F^s7$$!+T`%>,\"F^s$\"+SO0X5F-7%7$ $\"*u4Lj$F^s$\"+)R5E***F^s7$$\"+co#)**[F^s$\"+=@+16F-7$$\"+;33%e$F^s$ \"+wWd06F-7%7$$\"+?5/5iF^s$\"+7=m<(*F^s7$$\"++EVz&*F^sF_jq7$$\"+)=HXM) F^s$\"+!>G`6\"F-7%7$$\"+Ak#*[6F-Fdiq7$$\"+@Dl#[\"F-F_iq7$$\"+?e_f8F-$ \"+G(oa6\"F-7%7$$\"+#=RIm\"F-Fdhq7$$\"+S8<@?F-F_hq7$$\"+bLU&*=F-$\"+3M F96F-7%7$$\"+T)4b<#F-Fdgq7$$\"+hALhDF-F_gq7$$\"+6=0LCF-$\"+tm^76F-7%7$ $\"+Gw`*o#F-Fdfq7$$\"+ag$**4$F-F_fq7$$\"+mD*)pHF-$\"+*)y^56F-7%7$$\"+F !Rd?$F-Fdeq7$$\"+NiOOOF-F_eq7$$\"+YtI0NF-$\"+StZ36F-7%7$$\"+c4&Rs$F-Fd dq7$$\"+')eyqTF-F_dq7$$\"+d\"z#RSF-$\"+O1^16F-7%7$$\"+$z?QC%F-Fdcq7$$ \"+Hwa.ZF-F_cq7$$\"+,P)>d%F-$\"+@]n/6F-7%7$$\"+>'**\\w%F-Fdbq7$$\"+$Q+ ]B&F-F_bq7$$\"+JMj.^F-$\"+?@*H5\"F-7%7$$!+2PGE_F-$\"+yY*oJ\"F-7$$!+$H; Px%F-$\"+76U47F-7$$!+BX6Q[F-$\"+#>=`D\"F-7%7$$!+Gy%Rp%F-$\"+=zv?8F-7$$ !+%f?MD%F-$\"+syb07F-7$$!+Cvz7VF-$\"+vd__7F-7%7$$!+.SNgTF-$\"+ZC)\\K\" F-7$$!+TGQMPF-$\"+VLL,7F-7$$!+ez'zy$F-$\"+&z;KF-$\"+`!)y'>\"F-7$$!+1,wjKF-$\"+#y_fC\"F-7%7$$!+u$\\() 3$F-$\"+ogFM8F-7$$!+9Vs+FF-$\"+A(R?>\"F-7$$!+Y`GSFF-$\"+ZgBU7F-7%7$$!+ fZ*4b#F-$\"+Xq'*Q8F-7$$!+^t%e=#F-$\"+X([t=\"F-7$$!+lL_XhF^s$\"+Gm_% =\"F-7$$!+p7K6kF^s$\"+A/2O7F-7%7$$!+fx6')\\F^s$\"+<.<58F-7$$!*,-/x#F^s $\"+ta9;7F-7$$!+hxv-5F^s$\"+Py/g7F-7%7$$\"*C,/x#F^s$\"+ua9;7F-7$$\"+1x 6')\\F^s$\"+;.<58F-7$$\"+p[usOF^s$\"+G(eLJ\"F-7%7$$\"+76>XhF^sFb\\s7$$ \"+3DGW'*F^sF]\\s7$$\"+y:E&R)F^s$\"+#GO_K\"F-7%7$$\"+XDJ^6F-Fb[s7$$\"+ (Rm-[\"F-F][s7$$\"+c&*od8F-$\"+F\\>E8F-7%7$$\"+W&*yq;F-Fbjr7$$\"+y4U8? F-F]jr7$$\"+d(*H*)=F-$\"+@MfD8F-7%7$$\"+[t%e=#F-Fbir7$$\"+bZ*4b#F-F]ir 7$$\"+.tbCCF-$\"+!4)RC8F-7%7$$\"+6Vs+FF-Fbhr7$$\"+r$\\()3$F-F]hr7$$\"+ B1HgHF-$\"+\\A)GK\"F-7%7$$\"+)=&z;KF-Fbgr7$$\"+u+JDOF-F]gr7$$\"+bGQ&\\ $F-$\"+(\\97K\"F-7%7$$\"+SGQMPF-Fbfr7$$\"+-SNgTF-F]fr7$$\"+&>)[HSF-$\" +*=5&>8F-7%7$$\"+%f?MD%F-Fber7$$\"+Gy%Rp%F-F]er7$$\"+q3diXF-$\"+QF%yJ \"F-7%7$$\"+%H;Px%F-Fbdr7$$\"+3PGE_F-F]dr7$$\"+*\\9Z4&F-$\"+RVD;8F-7%7 $$!+u(>y@&F-$\"+vCvK:F-7$$!+E-=#y%F-$\"+Zfh99F-7$$!+!H\"eR[F-$\"+L_(>Y \"F-7%7$$!+?o#\\o%F-$\"+m#ek`\"F-7$$!+-;WiUF-$\"+c,\"4T\"F-7$$!+]&yYJ% F-$\"+!Q;#f9F-7%7$$!+5P%4:%F-$\"+\\&)QS:F-7$$!+MJzVPF-$\"+t)zpS\"F-7$$ !+3OD!z$F-$\"+G7Ac9F-7%7$$!+wS%eh$F-$\"+)*3YW:F-7$$!+!>hiA$F-$\"+Cv!HS \"F-7$$!+HHPmKF-$\"+tQ.`9F-7%7$$!+,)=)zIF-$\"+\")Q^[:F-7$$!+))[l4FF-$ \"+TX&))R\"F-7$$!+#=HIu#F-$\"+M\\w\\9F-7%7$$!+,pcVDF-$\"+#F-$\"+067&R\"F-7$$!+VO,?AF-$\"+7XlY9F-7%7$$!+;$o*3?F-$\"+@33b:F-7 $$!+;ACv;F-$\"+,wG#R\"F-7$$!+bJi'p\"F-$\"+s'>UW\"F-7%7$$!+!*[#3[\"F-$ \"+N[nb:F-7$$!+kSv]6F-$\"+(e$p\"R\"F-7$$!+aB(4<\"F-$\"+5,qV9F-7%7$$!+e #H\"=(*F^s$\"+(f$e\\:F-7$$!+#\\W82'F^s$\"+D[y(R\"F-7$$!+$RDlQ'F^s$\"+Z T))[9F-7%7$$!+Ae\"o/&F^s$\"+Y1[::F-7$$!*Q@M;#F^s$\"+wx)=V\"F-7$$!+[E%4 +\"F^s$\"+K&QTZ\"F-7%7$$\"*k?M;#F^s$\"+xx)=V\"F-7$$\"+md\"o/&F^s$\"+X1 [::F-7$$\"+:)f(RPF^s$\"+EY`@:F-7%7$$\"+BWMrgF^sF^^t7$$\"+(>H\"=(*F^sFi ]t7$$\"+tf?a%)F^s$\"+B@&\\`\"F-7%7$$\"+eSv]6F-F^]t7$$\"+%)[#3[\"F-Fi\\ t7$$\"+9$=\"e8F-$\"+&Rvm`\"F-7%7$$\"+7ACv;F-F^\\t7$$\"+6$o*3?F-Fi[t7$$ \"+5;%e)=F-$\"+g8_O:F-7%7$$\"+1_F$>#F-F^[t7$$\"+(*ocVDF-Fijs7$$\"+!eC' =CF-$\"+zIuN:F-7%7$$\"+&)[l4FF-F^js7$$\"+(z=)zIF-Fiis7$$\"+:u!H&HF-$\" +z)>Y`\"F-7%7$$\"+*=hiA$F-F^is7$$\"+uS%eh$F-Fihs7$$\"+w9E([$F-$\"+QGHL :F-7%7$$\"+LJzVPF-F^hs7$$\"+4P%4:%F-Figs7$$\"+7G5@SF-$\"+_A'=`\"F-7%7$ $\"+-;WiUF-F^gs7$$\"+?o#\\o%F-Fifs7$$\"+-BAaXF-$\"+k0SI:F-7%7$$\"+F-=# y%F-F^fs7$$\"+v(>y@&F-Fies7$$\"+\"Q$e'3&F-$\"+Wr&*G:F-7%7$$!+)\\!*)4_F -$\"+5hqZp;F-7%7$$!+=F uwYF-$\"+v$F-$\"+++p8;F-7$$!+z+_#z$F-$\"+3Mwj;F-7%7 $$!+DR+3OF-$\"+fHHe#F-$\"+*R&)Qg\"F-7$$!+!= 'y@AF-$\"+I\\nb;F-7%7$$!+.0!p+#F-$\"+4%yiw\"F-7$$!+H+Jx;F-$\"+XE9-;F-7 $$!+MgP(p\"F-$\"+/'eTl\"F-7%7$$!+h#)>$[\"F-$\"+XwUl!yq*fF^s$\"+%3#G6;F-7$$!+Rc)HO'F^s$\"+:w$=m\"F-7%7$$!+R+Y!4&F^s$\"+5 \\r@$[\"F-Fe^u7$$\"+Eu%*f8F-$\"+![+qu\"F-7%7 $$\"+C+Jx;F-Fj]u7$$\"+)\\+p+#F-Fe]u7$$\"+T'\\U)=F-$\"+)\\@su\"F-7%7$$ \"+\\PM)>#F-Fj\\u7$$\"+`$)\\QDF-Fe\\u7$$\"+;&\\YT#F-$\"+&ehnu\"F-7%7$$ \"+O-a;FF-Fj[u7$$\"+ZM$H2$F-Fe[u7$$\"+A5OZHF-$\"+\"pZfu\"F-7%7$$\"+S85 MKF-Fjjt7$$\"+AR+3OF-Fejt7$$\"+=,v![$F-$\"+a%4\\u\"F-7%7$$\"+xr*>v$F-F jit7$$\"+l'RF9%F-Feit7$$\"+0h19SF-$\"+%*=tVF-7$$ !+nY'yF%F-$\"+UbTC=F-7$$!+/iq=VF-$\"+8vWu=F-7%7$$!+d>wNTF-$\"+qBBo>F-7 $$!+()[(*ePF-$\"+;8C@=F-7$$!+wph%z$F-$\"+m^!>(=F-7%7$$!+eQn,OF-$\"+o1H r>F-7$$!+39VSKF-$\"+=I===F-7$$!+_lzqKF-$\"+>RRp=F-7%7$$!+1\\znIF-$\"+l n.u>F-7$$!+$yy;s#F-$\"+@pV:=F-7$$!+rE0ZFF-$\"+,13n=F-7%7$$!+0TGNDF-$\" +`M8w>F-7$$!+0!e:?#F-$\"+L-M8=F-7$$!+W*QHA#F-$\"+/BFl=F-7%7$$!+o%Ql+#F -$\"+J3#p(>F-7$$!+k?nx;F-$\"+bGb7=F-7$$!+O(3vp\"F-$\"+')Gek=F-7%7$$!+- =m'[\"F-$\"+]:zu>F-7$$!+_r\"\\9\"F-$\"+O@o9=F-7$$!+ZG()o6F-$\"+uSVm=F- 7%7$$!+J!))G')*F^s$\"+K?hk>F-7$$!+>deEfF^s$\"+a;'[#=F-7$$!+P-5UjF^s$\" +5+![(=F-7%7$$!+K:fA^F^s$\"+#[z'G>F-7$$!*GkcS\"F^s$\"+/Uzg=F-7$$!+4]12 5F^s$\"+B>S+>F-7%7$$\"*djcS\"F^sFfbv7$$\"+t9fA^F^sFabv7$$\"+/*4=$QF^s$ \"+9?*)Q>F-7%7$$\"+\\ceEfF^sFfav7$$\"+rz)G')*F^sFaav7$$\"+)eLRd)F^s$\" +*pOS&>F-7%7$$\"+Yr\"\\9\"F-Ff`v7$$\"+'zhm[\"F-Fa`v7$$\"+F-7%7$$\"+f?nx;F-Ff_v7$$\"+j%Ql+#F-Fa_v7$$\"+0=(R)=F-$\"+Suxd>F-7%7 $$\"+-!e:?#F-Ff^v7$$\"+,TGNDF-Fa^v7$$\"++u:7CF-$\"+#*Rdd>F-7%7$$\"+!yy ;s#F-Ff]v7$$\"+.\\znIF-Fa]v7$$\"+8hHVHF-$\"+)p/q&>F-7%7$$\"+19VSKF-Ff \\v7$$\"+cQn,OF-Fa\\v7$$\"+JkhvMF-$\"+7S?c>F-7%7$$\"+')[(*ePF-Ff[v7$$ \"+c>wNTF-Fa[v7$$\"+e/D3SF-$\"+FsCb>F-7%7$$\"+nY'yF%F-Ffju7$$\"+bP]pYF -Faju7$$\"+#fg2a%F-$\"+#3!>a>F-7%7$$\"+)[Ytz%F-Ffiu7$$\"+9Nl-_F-Faiu7$ $\"+;?$H2&F-$\"+$[wI&>F-7%7$$!+'[wh>&F-$\"+-^Uv@F-7$$!+:N#Q![F-$\"+;75 N?F-7$$!+6#>\\%[F-$\"+x)*4&3#F-7%7$$!+*GAKm%F-$\"+GjGy@F-7$$!+Mh9%G%F- $\"+!**RA.#F-7$$!+\\!z0K%F-$\"+dP\"G3#F-7%7$$!+E@%*HTF-$\"+4B2\"=#F-7$ $!+>ZzkPF-$\"+4SXH?F-7$$!+L2Z'z$F-$\"+/x`!3#F-7%7$$!+U\"zmf$F-$\"+!RaO =#F-7$$!+DhUXKF-$\"+G>(o-#F-7$$!+9,[sKF-$\"+y*y$y?F-7%7$$!+[_5kIF-$\"+ *eFe=#F-7$$!+S%o`s#F-$\"+H()pC?F-7$$!+UVN[FF-$\"+\"*4_w?F-7%7$$!+wx]LD F-$\"+bsB(=#F-7$$!+NVL.AF-$\"+j!*GB?F-7$$!+s^eBAF-$\"+gNHv?F-7%7$$!+M! *Q2?F-$\"+*ptr=#F-7$$!+)\\@on\"F-$\"+>ENB?F-7$$!+#Q(>(p\"F-$\"++$\\`2# F-7%7$$!+ZSu!\\\"F-$\"+EW*Q=#F-7$$!+3\\$39\"F-$\"+#*=jE?F-7$$!+i8#F-7$$!*k5P;\"F^s$\"+anI u?F-7$$!+10,75F^s$\"+]L'G6#F-7%7$$\"*%*4P;\"F^sF^dw7$$\"+OoyY^F^sFicw7 $$\"+GB>kQF^s$\"+Fr'z9#F-7%7$$\"+\"fM<'eF^sF^cw7$$\"+H!Rx#**F^sFibw7$$ \"+kIoH')F^s$\"+@(*[j@F-7%7$$\"+,\\$39\"F-F^bw7$$\"+TSu!\\\"F-Fiaw7$$ \"+[>%eO\"F-$\"+Y:Mn@F-7%7$$\"+$\\@on\"F-F^aw7$$\"+H!*Q2?F-Fi`w7$$\"+q \\i%)=F-$\"+sPBo@F-7%7$$\"+JVL.AF-F^`w7$$\"+rx]LDF-Fi_w7$$\"+9$*y5CF-$ \"+-,Do@F-7%7$$\"+P%o`s#F-F^_w7$$\"+X_5kIF-Fi^w7$$\"+1QTSHF-$\"+3!zy;# F-7%7$$\"+BhUXKF-F^^w7$$\"+R\"zmf$F-Fi]w7$$\"+6hjrMF-$\"+UEFn@F-7%7$$ \"+=ZzkPF-F^]w7$$\"+D@%*HTF-Fi\\w7$$\"+tY].SF-$\"+aL]m@F-7%7$$\"+Mh9%G %F-F^\\w7$$\"+*GAKm%F-Fi[w7$$\"+9/^NXF-$\"+w,il@F-7%7$$\"+;N#Q![F-F^[w 7$$\"+([wh>&F-Fijv7$$\"+j$yt1&F-$\"+Q&F-$\"+mYU)Q#F- 7$$!+fC`4[F-$\"+%GaJC#F-7$$!+I.hY[F-$\"+)*Hl$H#F-7%7$$!+Ka&yl%F-$\"+8y (4R#F-7$$!+!*H^*G%F-$\"+P6gSAF-7$$!+d(oAK%F-$\"+ldd\"H#F-7%7$$!+C:D#F-7$$!+Nld4jF^s$\"+8h[+BF-7%7$$!+LfQl^F^s$\"+ic@WBF-7$$!)F ?x(*F^s$\"+)GjtG#F-7$$!+]*ys,\"F^s$\"+e-,DBF-7%7$$\")e>x(*F^sFfex7$$\" +seQl^F^sFaex7$$\"+2;b!*QF^s$\"+K[CdBF-7%7$$\"+.29.eF^sFfdx7$$\"+LR\"o)F^s$\"+fZ#HP#F-7%7$$\"+IUWO6F-$\"+ervQAF-7$$\"+7 Z8&\\\"F-$\"+#z@GR#F-7$$\"+Y2Lp8F-$\"+W.SxBF-7%7$$\"+\"*e6v;F-Ffbx7$$ \"+JY44?F-Fabx7$$\"+W\"Rf)=F-$\"+\\dhyBF-7%7$$\"+3B+/AF-Ffax7$$\"+%zRG `#F-Faax7$$\"+/lF5CF-$\"+^7$)yBF-7%7$$\"+#ztys#F-Ff`x7$$\"+\"*)*fhIF-F a`x7$$\"+!>t%QHF-$\"+CmiyBF-7%7$$\"+&4r#\\KF-Ff_x7$$\"+nT$Gf$F-Fa_x7$$ \"+]8hoMF-$\"+l2=yBF-7%7$$\"+>`cpPF-Ff^x7$$\"+B:&F-Fa\\x7$$\"+%o&fi]F-$\"+g%>g P#F-7%7$$!+b&)\\&=&F-$\"+G-)4g#F-7$$!+X9]9[F-$\"+a8l^CF-7$$!+-%f\"[[F- $\"+f=`-DF-7%7$$!+2BL`YF-$\"+9^B.EF-7$$!+:h.%H%F-$\"+okR\\CF-7$$!+X9vB VF-$\"+A$o1]#F-7%7$$!+A\"H87%F-$\"+$3*H0EF-7$$!+AxStPF-$\"+*\\KtW#F-7$ $!+d.P*z$F-$\"+Q$H*)\\#F-7%7$$!+%ek**e$F-$\"+.M.2EF-7$$!+#oS@D$F-$\"+z \")fXCF-7$$!+&>L[F$F-$\"+D6W(\\#F-7%7$$!+'\\b+1$F-$\"+n]@3EF-7$$!+#>=% HFF-$\"+:lTWCF-7$$!+@i\")\\FF-$\"+2=T'\\#F-7%7$$!+nI-LDF-$\"+$pX%3EF-7 $$!+V!>Q?#F-$\"+*)e=WCF-7$$!+;EwBAF-$\"+\"Q4i\\#F-7%7$$!+lWR6?F-$\"+_o !pg#F-7$$!+ng\"Gn\"F-$\"+IZsXCF-7$$!+F5v&p\"F-$\"+.1b(\\#F-7%7$$!+/(G' *\\\"F-$\"+8Sj,EF-7$$!+]-&>8\"F-$\"+pv*4X#F-7$$!+#3\"[k6F-$\"+R_*>]#F- 7%7$$!+N:(Q+\"F-$\"+CVN(e#F-7$$!+0%e2v&F^s$\"+esFlCF-7$$!+$[PwH'F^s$\" +.v98DF-7%7$$!+f-&*z^F^s$\"+!QwDb#F-7$$!),x?$)F^s$\"+-_0+DF-7$$!+ahbA5 F^s$\"+$35p`#F-7%7$$\")Kw?$)F^s$\"+._0+DF-7$$\"+)>]*z^F^s$\"+zjd_DF-7$ $\"+'QWB\"RF^s$\"+C*)omDF-7%7$$\"+O$e2v&F^sFbfy7$$\"+G:(Q+\"F-F]fy7$$ \"+QX&)G()F^s$\"+\\OO#e#F-7%7$$\"+W-&>8\"F-Fbey7$$\"+)pG'*\\\"F-F]ey7$ $\"+*3]HP\"F-$\"+*=/ue#F-7%7$$\"+ig\"Gn\"F-Fbdy7$$\"+gWR6?F-F]dy7$$\"+ t1s()=F-$\"+>)Q*)e#F-7%7$$\"+R!>Q?#F-Fbcy7$$\"+jI-LDF-F]cy7$$\"+7rT5CF -$\"+.EM*e#F-7%7$$\"+*==%HFF-Fbby7$$\"+$\\b+1$F-F]by7$$\"+qLGPHF-$\"+1 NG*e#F-7%7$$\"+!oS@D$F-Fbay7$$\"+#ek**e$F-F]ay7$$\"+a]PmMF-$\"+ZG(*)e# F-7%7$$\"+@xStPF-Fb`y7$$\"+@\"H87%F-F]`y7$$\"+rtj'*RF-$\"+%Q%\\)e#F-7% 7$$\"+:h.%H%F-Fb_y7$$\"+2BL`YF-F]_y7$$\"+ByYFXF-$\"+!)G*ye#F-7%7$$\"+Y 9]9[F-Fb^y7$$\"+c&)\\&=&F-F]^y7$$\"+_+^e]F-$\"+M%*>(e#F-7%7$$!+K9A\"=& F-$\"+P'oJ\"GF-7$$!+o&y(=[F-$\"+xb^gEF-7$$!+oca\\[F-$\"+x!)o6FF-7%7$$! +84d\\YF-$\"+W*R^\"GF-7$$!+4vz(H%F-$\"+qUaeEF-7$$!+PD-DVF-$\"+)*o.5FF- 7%7$$!+LhH=TF-$\"+%*y(o\"GF-7$$!+62WwPF-$\"+?j!ol#F-7$$!+9AV+QF-$\"+/c b3FF-7%7$$!+$o:ze$F-$\"+<(Q#=GF-7$$!+$e*=aKF-$\"+(\\Xal#F-7$$!+A0dvKF- $\"+ovP2FF-7%7$$!+`yGfIF-$\"+g$))*=GF-7$$!+Oe=IFF-$\"+aepaEF-7$$!+0r4] FF-$\"+E8s1FF-7%7$$!+)fdQ`#F-$\"+&G.(=GF-7$$!+7X)H?#F-$\"+H4)\\l#F-7$$ !++uXBAF-$\"+8:(pq#F-7%7$$!+=o49?F-$\"+6C^;GF-7$$!+9P6q;F-$\"+.=&F^s$\"+q;BhFF-7 $$!)hHhrF^s$\"+WDX7FF-7$$!+'*fnF5F^s$\"+&>8'[FF-7%7$$\")#*GhrF^s$\"+XD X7FF-7$$\"+Q\\a\">&F^s$\"+p;BhFF-7$$\"+pBhIRF^s$\"+R.FwFF-7%7$$\"+W2@/ dF^sF^hz7$$\"+)GE&35F-Figz7$$\"+x\"[@x)F^s$\"+\\@#=z#F-7%7$$\"+vy[F6F- F^gz7$$\"+o54/:F-Fifz7$$\"+Defw8F-$\"+mYO(z#F-7%7$$\"+4P6q;F-F^fz7$$\" +8o49?F-Fiez7$$\"+Y$G)*)=F-$\"+8L@*z#F-7%7$$\"+3X)H?#F-F^ez7$$\"+%fdQ` #F-Fidz7$$\"+L#e5T#F-$\"+4+!)*z#F-7%7$$\"+Le=IFF-F^dz7$$\"+]yGfIF-Ficz 7$$\"+lPpOHF-$\"+!4t)*z#F-7%7$$\"+#e*=aKF-F^cz7$$\"+\"o:ze$F-Fibz7$$\" +!)*)ykMF-$\"+c#z'*z#F-7%7$$\"+52WwPF-F^bz7$$\"+KhH=TF-Fiaz7$$\"+&*)fU *RF-$\"+`TJ*z#F-7%7$$\"+4vz(H%F-F^az7$$\"+84d\\YF-Fi`z7$$\"+*etW_%F-$ \"+cY#))z#F-7%7$$\"+p&y(=[F-F^`z7$$\"+L9A\"=&F-Fi_z7$$\"+qh/b]F-$\"+B/ C)z#F-7%7$$!+'zyv<&F-$\"+eF0DIF-7$$!+07UA[F-$\"+)3%opGF-7$$!+qBw][F-$ \"+r-3@HF-7%7$$!++z[YYF-$\"+]qvEIF-7$$!+A0)3I%F-$\"+'zzz'GF-7$$!+B))3E VF-$\"+\\kj>HF-7%7$$!+&*G'f6%F-$\"+j@>GIF-7$$!+\\RxyPF-$\"+$oWl'GF-7$$ !+gEE,QF-$\"+O=S=HF-7%7$$!+NTb'e$F-$\"+!f3#HIF-7$$!+J6bbKF-$\"+c#Gb'GF -7$$!+z_1wKF-$\"+Qi^IF-7$ $!+.W9B6F-$\"+YzlvGF-7$$!+>Juh6F-$\"+,S(f#HF-7%7$$!+'y\\E,\"F-$\"+Ze9. IF-7$$!+\"*e(Hm&F^s$\"+**4f\"*GF-7$$!+Uyu!G'F^s$\"+U41QHF-7%7$$!+`B\"4 ?&F^s$\"+mu7qHF-7$$!)2cCiF^s$\"+!Q4Y#HF-7$$!+ubbK5F^s$\"+ow:gHF-7%7$$ \")SbCiF^sFjj[l7$$\"+!H74?&F^sFej[l7$$\"+(G9h%RF^s$\"+Xe'f)HF-7%7$$\"+ @e(Hm&F^sFji[l7$$\"+!y\\E,\"F-Fei[l7$$\"+W!3:\"))F^s$\"+C6J,IF-7%7$$\" +(RWJ7\"F-Fjh[l7$$\"+XXV3:F-Feh[l7$$\"+Lx>!Q\"F-$\"+g=H2IF-7%7$$\"+\"p ]rm\"F-Fjg[l7$$\"+J)fq,#F-Feg[l7$$\"+Qx:#*=F-$\"+5oW4IF-7%7$$\"+EYl,AF -Fjf[l7$$\"+wu=NDF-Fef[l7$$\"+;G37CF-$\"+qQ@5IF-7%7$$\"+OrKIFF-Fje[l7$ $\"+Yl9fIF-Fee[l7$$\"+i`eOHF-$\"+O4T5IF-7%7$$\"+H6bbKF-Fjd[l7$$\"+LTb' e$F-Fed[l7$$\"+w(RPY$F-$\"+34K5IF-7%7$$\"+[RxyPF-Fjc[l7$$\"+%*G'f6%F-F ec[l7$$\"+3XW#*RF-$\"+/R05IF-7%7$$\"+A0)3I%F-Fjb[l7$$\"++z[YYF-Feb[l7$ $\"+;Q/AXF-$\"+N6m4IF-7%7$$\"+17UA[F-Fja[l7$$\"+(zyv<&F-Fea[l7$$\"+9A8 _]F-$\"+MB<4IF-7%7$$!+A1^u^F-$\"+$p$oOKF-7$$!+y$*[D[F-$\"+&y0\"zIF-7$$ !+)f6=&[F-$\"+lMnIJF-7%7$$!+*z.Sk%F-$\"+'oP\"QKF-7$$!+BYO.VF-$\"+#z^w2 $F-7$$!+EL'pK%F-$\"+m*H%HJF-7%7$$!+s9B9TF-$\"+\\8HRKF-7$$!+s`]!y$F-$\" +H\")\\wIF-7$$!+6j)=!QF-$\"++-VGJF-7%7$$!+Ynw&e$F-$\"+u'))*RKF-7$$!+?& QjD$F-$\"+/3!e2$F-7$$!+9JNwKF-$\"+K*>y7$F-7%7$$!+L\"4&fIF-$\"+$**p*RKF -7$$!+bX'*HFF-$\"+&[>e2$F-7$$!+;g,]FF-$\"+Tj$y7$F-7%7$$!+M1*o`#F-$\"+P ,wQKF-7$$!+w9&**>#F-$\"+T$Hq2$F-7$$!+q+OAAF-$\"+V?*)GJF-7%7$$!+s!y,-#F -$\"+HzRNKF-7$$!+gC.k;F-$\"+\\:R!3$F-7$$!+`2q#p\"F-$\"+&pe<8$F-7%7$$!+ $f/E^\"F-$\"+G*pxA$F-7$$!+hV(*=6F-$\"+]&>!)3$F-7$$!+8e_g6F-$\"+1z&z8$F -7%7$$!+\"[)H;5F-$\"+z_E6KF-7$$!+U*)[EcF^s$\"+*>CX5$F-7$$!+NK5viF^s$\" ++oJ]JF-7%7$$!+#3!e3_F^s$\"+X;AzJF-7$$!)yydaF^s$\"+LycOJF-7$$!+E*er.\" F^s$\"+lEdrJF-7%7$$\")5ydaF^s$\"+MycOJF-7$$\"+?+e3_F^s$\"+W;AzJF-7$$\" +]ETfRF^s$\"+Mov&>$F-7%7$$\"+s))[EcF^s$\"++U_/JF-7$$\"+v%)H;5F-$\"+y_E 6KF-7$$\"+5(Qs%))F^s$\"+Ow$3@$F-7%7$$\"+bV(*=6F-Fbj\\l7$$\"+(e/E^\"F-F ]j\\l7$$\"+\\\"4PQ\"F-$\"+&f%>KF-7%7$$\"+s9&**>#F-Fbh\\l7$$\"+I1*o`#F-F]h \\l7$$\"+*G+MT#F-$\"+]8f?KF-7%7$$\"+_X'*HFF-Fbg\\l7$$\"+I\"4&fIF-F]g\\ l7$$\"+-O'o$HF-$\"+&f24A$F-7%7$$\"+=&QjD$F-Fbf\\l7$$\"+Wnw&e$F-F]f\\l7 $$\"+KZ8jMF-$\"+pB\"4A$F-7%7$$\"+s`]!y$F-Fbe\\l7$$\"+r9B9TF-F]e\\l7$$ \"+qZ5\"*RF-$\"+))=t?KF-7%7$$\"+BYO.VF-Fbd\\l7$$\"+*z.Sk%F-F]d\\l7$$\" +795?XF-$\"+IMU?KF-7%7$$\"+z$*[D[F-Fbc\\l7$$\"+B1^u^F-F]c\\l7$$\"+6Aq \\]F-$\"+P\"=+A$F-7%7$$!+P\"e><&F-$\"+**G5[MF-7$$!+j=/G[F-$\"+6#R()G$F -7$$!+o2q_[F-$\"+v#Q/M$F-7%7$$!+?b/UYF-$\"+BDK\\MF-7$$!+-HK0VF-$\"+(e> vG$F-7$$!+q?mFVF-$\"+\"3(QRLF-7%7$$!+7g,8TF-$\"+>R@]MF-7$$!+K3s\"y$F-$ \"+\">GmG$F-7$$!+-yK-QF-$\"+*H5'QLF-7%7$$!+9\"eae$F-$\"+;Rh]MF-7$$!+_r kcKF-$\"+%>GiG$F-7$$!+viYwKF-$\"+&Hf#QLF-7%7$$!+neFgIF-$\"+z!\\-X$F-7$ $!+@y>HFF-$\"+JIf'G$F-7$$!+0et\\FF-$\"+2&z&QLF-7%7$$!+;5()QDF-$\"+(p>' [MF-7$$!+%4rz>#F-$\"+8CA)G$F-7$$!+TRl@AF-$\"+SW**RLF-7%7$$!+IIPB?F-$\" +!)*HZW$F-7$$!+-v$3m\"F-$\"+I@6#H$F-7$$!+ocj\"p\"F-$\"+S;GVLF-7%7$$!+` #pl^\"F-$\"+zvYOMF-7$$!+,(4]6\"F-$\"+JXP+LF-7$$!+;3Uf6F-$\"+=v\"*\\LF- 7%7$$!+Kw_>5F-$\"+BB`>MF-7$$!+Nu>%f&F^s$\"+(y4tJ$F-7$$!+6[\"4F'F^s$\"+ 4qWiLF-7%7$$!+#fI\\@&F^s$\"+`5[)Q$F-7$$!)otA[F^s$\"+d5O[LF-7$$!+SkZT5F ^s$\"+23)GQ$F-7%7$$\"),tA[F^sFb^^l7$$\"+H0$\\@&F^sF]^^l7$$\"+\"[J4(RF^ s$\"+N$GcS$F-7%7$$\"+mt>%f&F^s$\"+)y4tJ$F-7$$\"+Dw_>5F-$\"+AB`>MF-7$$ \"+H!o'z))F^s$\"+*)eS?MF-7%7$$\"+&p4]6\"F-Fb\\^l7$$\"+Z#pl^\"F-F]\\^l7 $$\"+w**4(Q\"F-$\"+Z03FMF-7%7$$\"+(\\P3m\"F-Fb[^l7$$\"+DIPB?F-F][^l7$$ \"+.()=(*=F-$\"+BS\")HMF-7%7$$\"+!4rz>#F-Fbj]l7$$\"+75()QDF-F]j]l7$$\" +j)R\\T#F-$\"+iw$4V$F-7%7$$\"+=y>HFF-Fbi]l7$$\"+keFgIF-F]i]l7$$\"+]GXP HF-$\"+2/PJMF-7%7$$\"+]rkcKF-Fbh]l7$$\"+7\"eae$F-F]h]l7$$\"+7z*GY$F-$ \"+6RYJMF-7%7$$\"+K3s\"y$F-Fbg]l7$$\"+6g,8TF-F]g]l7$$\"+hz;!*RF-$\"+H8 OJMF-7%7$$\"+-HK0VF-Fbf]l7$$\"+?b/UYF-F]f]l7$$\"+<&z&=XF-$\"+\"HF6V$F- 7%7$$\"+k=/G[F-Fbe]l7$$\"+Q\"e><&F-F]e]l7$$\"+GppZ]F-$\"+iazIMF-7%7$$! +Rf')p^F-$\"+GSMfOF-7$$!+hS8I[F-$\"+92b)\\$F-7$$!+g-W`[F-$\"+#3].b$F-7 %7$$!+hsaSYF-$\"+\")RMgOF-7$$!+i6#oI%F-$\"+h2b(\\$F-7$$!+,@?GVF-$\"+KG [\\NF-7%7$$!+[?C7TF-$\"+d+*4m$F-7$$!+'z%\\#y$F-$\"+&o/p\\$F-7$$!+\"\\5 E!QF-$\"+tv\"*[NF-7%7$$!+g![be$F-$\"+L96hOF-7$$!+1sbcKF-$\"+4Ly'\\$F-7 $$!+wKVwKF-$\"+M4\")[NF-7%7$$!+=`OhIF-$\"+J3UgOF-7$$!+q$3\"GFF-$\"+6RZ (\\$F-7$$!+.(R$\\FF-$\"+,eT\\NF-7%7$$!+NF0TDF-$\"+^eReOF-7$$!+v$*y&>#F -$\"+\"*))\\*\\$F-7$$!+&y&)3A#F-$\"+gU;^NF-7%7$$!+zjeE?F-$\"+eS,aOF-7$ $!+`Tid;F-$\"+%o!)Q]$F-7$$!+R,f!p\"F-$\"+CO$[b$F-7%7$$!+u@J?:F-$\"+&Q' =XOF-7$$!+!ym76\"F-$\"+d$3F^$F-7$$!+A$G%e6F-$\"+hH%=c$F-7%7$$!+o&)QA5F -$\"+M;%zi$F-7$$!+q!)elbF^s$\"+3J&*HNF-7$$!+Y\\#zE'F^s$\"+M(fWd$F-7%7$ $!+#zX-A&F^s$\"+H$zyf$F-7$$!)o@\"H%F^s$\"+8a,gNF-7$$!+UI^X5F^s$\"+f)*4 %f$F-7%7$$\"),@\"H%F^sF^`_l7$$\"+HdC?_F^sFi__l7$$\"+$Q&*4)RF^s$\"+>#ob h$F-7%7$$\"+,!)elbF^s$\"+4J&*HNF-7$$\"+i&)QA5F-$\"+L;%zi$F-7$$\"+i/74* )F^s$\"+$)z,IOF-7%7$$\"+tnE66F-F^^_l7$$\"+p@J?:F-Fi]_l7$$\"+f=N!R\"F-$ \"+?j&pj$F-7%7$$\"+[Tid;F-F^]_l7$$\"+ujeE?F-Fi\\_l7$$\"+Iqy**=F-$\"+Tt &*ROF-7%7$$\"+r$*y&>#F-F^\\_l7$$\"+JF0TDF-Fi[_l7$$\"+@dk;CF-$\"+=oDTOF -7%7$$\"+n$3\"GFF-F^[_l7$$\"+:`OhIF-Fij^l7$$\"+d@HQHF-$\"+NY!=k$F-7%7$ $\"+/sbcKF-F^j^l7$$\"+e![be$F-Fii^l7$$\"+5p'HY$F-$\"+$*G)>k$F-7%7$$\"+ &z%\\#y$F-F^i^l7$$\"+Z?C7TF-Fih^l7$$\"+%*Hd*)RF-$\"+%*=&>k$F-7%7$$\"+i 6#oI%F-F^h^l7$$\"+hsaSYF-Fig^l7$$\"+g0Uxq$F-7$$!+I.gGVF-$\"+LmpfPF-7%7$$!+[` %=6%F-$\"+vOkrQF-7$$!+'\\\"*Gy$F-$\"+*p.tq$F-7$$!+_ev-QF-$\"+S?LfPF-7% 7$$!+@#pfe$F-$\"+dD]rQF-7$$!+Xg8cKF-$\"+<[W2PF-7$$!+z*yiF$F-$\"+=gXfPF -7%7$$!++3riIF-$\"+\")Q]qQF-7$$!+))GwEFF-$\"+$\\V%3PF-7$$!+tQ&)[FF-$\" +#*zKgPF-7%7$$!+DcPVDF-$\"+a\\5oQF-7$$!+'[mM>#F-$\"+?C%3r$F-7$$!+&\\z+ A#F-$\"+9iQiPF-7%7$$!+O]xH?F-$\"+!*[EjQF-7$$!+(\\NWl\"F-$\"+%[#o:PF-7$ $!+*Qz&*o\"F-$\"+*)>SmPF-7%7$$!+!oFQ_\"F-$\"+Qs$R&QF-7$$!+u7v26F-$\"+O ,,DPF-7$$!+RZad6F-$\"+$\\FPx$F-7%7$$!+mv#\\-\"F-$\"+4h[OQF-7$$!+#4)>Sb F^s$\"+l7YUPF-7$$!+cc\"fE'F^s$\"+HOO'y$F-7%7$$!+EotC_F^s$\"++`R2QF-7$$ !)M6UQF^s$\"+u?brPF-7$$!+O8G\\5F^s$\"+RRC0QF-7%7$$\")m5UQF^sFja`l7$$\" +kntC_F^sFea`l7$$\"+(Rc)*)RF^s$\"+#fmb#QF-7%7$$\"+C!)>SbF^sFj``l7$$\"+ gv#\\-\"F-Fe``l7$$\"+kF!f$*)F^s$\"+@XnRQF-7%7$$\"+o7v26F-Fj_`l7$$\"+vw #Q_\"F-Fe_`l7$$\"+rZX$R\"F-$\"+Av#o%QF-7%7$$\"+\"\\NWl\"F-Fj^`l7$$\"+J ]xH?F-Fe^`l7$$\"+N@R->F-$\"+R$z+&QF-7%7$$\"+\"[mM>#F-Fj]`l7$$\"+@cPVDF -Fe]`l7$$\"+GNZ=CF-$\"+u?b^QF-7%7$$\"+&)GwEFF-Fj\\`l7$$\"+(z5F1$F-Fe\\ `l7$$\"+p?LRHF-$\"+tT@_QF-7%7$$\"+Vg8cKF-Fj[`l7$$\"+>#pfe$F-Fe[`l7$$\" +)>!HjMF-$\"+tYZ_QF-7%7$$\"+&\\\"*Gy$F-Fjj_l7$$\"+Z`%=6%F-Fej_l7$$\"+1 &o#*)RF-$\"+>2^_QF-7%7$$\"+$)y\"zI%F-Fji_l7$$\"+R0XRYF-Fei_l7$$\"+N^d; XF-$\"+2SS_QF-7%7$$\"+$*p\"=$[F-Fjh_l7$$\"+4I=o^F-Feh_l7$$\"+SrvW]F-$ \"+Cd>_QF-7%7$$!+]I'o;&F-$\"+8mR\"3%F-7$$!+^p8L[F-$\"+$R.'=RF-7$$!+!*y ^a[F-$\"+ka`qRF-7%7$$!+#y.(QYF-$\"+Hd*>3%F-7$$!+SYm3VF-$\"+xU+=RF-7$$! +#)G()GVF-$\"+D9,qRF-7%7$$!+[1x6TF-$\"+1R>#3%F-7$$!+'>mHy$F-$\"++h!y\" RF-7$$!+fKy-QF-$\"+Ft$)pRF-7%7$$!+M\\m'e$F-$\"+*H/=3%F-7$$!+K.WbKF-$\" +2d>=RF-7$$!+x[-wKF-$\"+P#z,(RF-7%7$$!+?vDkIF-$\"+vJ^!3%F-7$$!+oh@DFF- $\"+Jo[>RF-7$$!+U+I[FF-$\"+D@IrRF-7%7$$!+#)=zXDF-$\"+>.wxSF-7$$!+G-0\" >#F-$\"+(oRA#RF-7$$!+^QD>AF-$\"+uzktRF-7%7$$!+>v!H.#F-$\"+.X\\sSF-7$$! +9II^;F-$\"+.b]FRF-7$$!+^Ph)o\"F-$\"+nn(z(RF-7%7$$!+.t6F:F-$\"+]\"GF1% F-7$$!+^;Y/6F-$\"+c=FPRF-7$$!+#>kn:\"F-$\"+Bnc&)RF-7%7$$!+&e&=F5F-$\"+ Px:XSF-7$$!+'*yhF-$\"+*o$=gSF-7%7$$ \"+C-0\">#F-Fb_al7$$\"+y=zXDF-F]_al7$$\"+fyQ?CF-$\"+(>E=1%F-7%7$$\"+lh @DFF-Fb^al7$$\"+mHy$F-Fb\\al 7$$\"+Z1x6TF-F]\\al7$$\"+07@*)RF-$\"+DJ/jSF-7%7$$\"+SYm3VF-Fb[al7$$\"+ #y.(QYF-F][al7$$\"+$)3+;XF-$\"+&\\#*H1%F-7%7$$\"+_p8L[F-Fbj`l7$$\"+^I' o;&F-F]j`l7$$\"+]jtV]F-$\"+_r$G1%F--%&COLORG6&Fi[l$\"\"(F\\\\l$\"#&)! \"#$\"#vF\\\\bl-F$6$7U7$F($\"+\"RR@6\"F-7$F/$\"+8$)*e1\"F-7$F4$\"+t2fD 5F-7$F9$\"+E'\\$\"+L`hV$*F^s7$FC$\"+Y1k')))F^s7$FH$\"+ka+i% )F^s7$FM$\"+<`G@!)F^s7$FR$\"+)p6Vc(F^s7$FW$\"+hU_2rF^s7$Ffn$\"+IhAOmF^ s7$F[o$\"+'3.)>iF^s7$F`o$\"+24U\\dF^s7$Feo$\"+1QDv_F^s7$Fjo$\"+58O;[F^ s7$F_p$\"+PO!yR%F^s7$Fdp$\"+u#Hv*QF^s7$Fip$\"+mYCrMF^s7$F^q$\"+d8-sHF^ s7$Fcq$\"+V+bEDF^s7$Fhq$\"+#H@I.#F^s7$F]r$\"+G\\1d:F^s7$Fbr$\"+mek^5F^ s7$Fgr$\"+ES:YdF[]l7$F\\s$\"+#\\$*f2$F[]l7$Fbs$\"+j01<=!#77$Fgs$\"+lN_ FHF[]l7$F\\t$\"+nbt*>'F^s7$Fbx$\"+Lg\"ok'F^s7$Fgx$\"+O)fL6(F^s7$F\\y $\"+K([8c(F^s7$Fay$\"+o9@=!)F^s7$Ffy$\"+vm5q%)F^s7$F[z$\"+3bP%)))F^s7$ F`z$\"+(p#4e$*F^s7$Fez$\"+%>m3y*F^s7$Fjz$\"+'4sI-\"F-7$F_[l$\"+u`/m5F- 7$Fd[lFc\\blFf[l-%+AXESLABELSG6$%\"xG%!G-%%VIEWG6$;$!+++++bF-$\"+++++b F-;$!+++++?F^s$\"+++++UF-" 2 638 362 362 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 402 2 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT 359 8 "Code for" }{TEXT -1 1 " " }{TEXT 280 15 "homogeneous_ode " }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 493 78 "You must execute th is function here in order to use it later in the worksheet!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4066 " homogeneous_ode := proc()\noption `Copyright \2511997-2001 Brian E. Bl ank, All Rights Reserved.`:\nlocal xx, yy, x_0, y_0, expr, expr_uv, n u, eqn, eqn2, eqn3, eqn4, eqn5, eqn6, Eqn5, u_, v_, cc, LIST1, LIST2, \+ LIST3, NF1, NF2, NF3, jj, kk, nu_integrand, xx_integrand, xi,eta;\nglo bal _C;\nreadlib(isolate):\n\nif nargs < 1 or nargs > 2 then \nERROR(` homogeneous_ode expects one or two arguments.`);\nfi:\n\nif nargs = 1 \+ and not type(args[1],equation) then \nERROR(`homogeneous_ode expects i ts argument to be an equation.`):\nelif nargs = 2 and (not type(args[1 ],equation) or not type(args[2],equation))\nthen\nERROR(`homogeneous_o de expects its arguments to be equations.`):\nfi:\n\nif nargs = 2 then \nif (not type( lhs(args[2]),function) or not type(op(0,lhs(args[2])), name) or nops( lhs(args[2]) ) <> 1 or not type(rhs(args[2]),algebraic ))\nthen ERROR(`homogeneous_ode expects its second argument to be of t he form y(a) = c.`):\nelse \ny_0 := rhs(args[2]);\nx_0 := op(1,lhs(arg s[2])):\nyy := op(0,lhs(args[2])):\nfi:\nfi:\n \n\nif not has(lhs(args [1]), diff) then\nERROR(`homogeneous_ode expects its first argument to be of the form diff(y(x),x)=F(x,y(x)).`):\nelif nops(op(1,lhs(args[1] ))) <> 1\nthen\nERROR(`homogeneous_ode expects its first argument to b e of the form diff(y(x),x)=F(x,y(x)) where y(x) is a function of one v ariable.`):\nelif not type(op(1,(op(1,lhs(args[1])))),name)\nthen\nERR OR(`homogeneous_ode expects its first argument to be of the form diff( y(x),x)=F(x,y(x)) where y(x) is a function of one variable and x is a \+ name of a variable.`):\nelse\nxx := op(1,(op(1,lhs(args[1])))):\nexpr \+ := rhs(args[1]):\nfi;\n\n\nif not type(rhs(args[1]), algebraic) then\n ERROR(`homogeneous_ode expects its first argument to be of the form di ff(y(x),x)=F(x,y(x)).`):\nfi:\n\nif nargs = 2 and op(0,op(1,lhs(args[1 ])))<>yy\nthen\nERROR(`homogeneous_ode expects the dependent variable \+ names in the first two arguments to be the same.`):\nfi:\n\nif nargs = 1 then yy := op(0,op(1,lhs(args[1]))): fi:\n\nexpr_uv := subs(\{xx = \+ u_, yy(xx)=v_\},expr):\n\nif simplify(expr_uv - subs(\{u_=t*u_,v_=t*v_ \},expr_uv)) <> 0 then \nERROR(`The differential equation does not app ear to be homogeneous.`);\nfi:\n\n\neqn := args[1]:\neqn2 := DEtools[D changevar](yy(xx)=xx*nu(xx) , [eqn], xx );\neqn2 := expand(lhs(eqn2))= rhs(eqn2):\neqn3 := diff(nu(xx),xx) = solve(eqn2, diff(nu(xx),xx)):\ne qn4 := lhs(eqn3) = normal(rhs(eqn3));\n\n\nif type(factor(numer(rhs(eq n4))),`*`) then\n LIST1 := [op(factor(numer(rhs(eqn4))))];\nelse\n \+ LIST1 := [numer(rhs(eqn4))];\nfi;\nif type(denom(rhs(eqn4)),`*`) th en\n LIST2 := map(z->z^(-1),[op(factor(denom(rhs(eqn4))))]);\nelse\n LIST2 := [denom(rhs(eqn4))^(-1)];\nfi;\nNF1 := nops(LIST1);\nNF2 : = nops(LIST2); \nLIST3 := [];\nfor kk from 1 to NF1 do\nif type(LIST1[ kk], `^`) and nops(op(1,LIST1[kk])) > 1 and type(op(1,LIST1[kk]),`*`) \+ then\n for jj from 1 to nops(op(1,LIST1[kk])) do\n LIST3 := [op(LI ST3),op(jj,op(1,LIST1[kk]))^op(2,LIST1[kk])];\n od;\nelse\nLIST3 := \+ [op(LIST3),LIST1[kk]];\nfi;\nod; \n\nfor kk from 1 to NF2 do\nif type( LIST2[kk], `^`) and nops(op(1,LIST2[kk])) > 1 and type(op(1,LIST2[kk]) ,`*`) then\n for jj from 1 to nops(op(1,LIST2[kk])) do\n LIST3 := \+ [op(LIST3),op(jj,op(1,LIST2[kk]))^(-op(2,LIST2[kk]))];\n od:\nelse\n LIST3 := [op(LIST3),LIST2[kk]];\nfi;\nod;\n\nNF3 := nops(LIST3);\n\nnu _integrand := 1;\nxx_integrand := 1;\n\nfor jj from 1 to NF3 do\nif ha s(LIST3[jj],nu(xx) ) \n then nu_integrand := nu_integrand*LIST3[jj]^ (-1);\nelse\n xx_integrand := xx_integrand*LIST3[jj];\nfi;\nod;\n\n \n\nnu_integrand := subs(nu(xx)=nu,nu_integrand);\n\nif nargs = 1\nor \+ (nargs = 2 and x_0 = 0)\nthen\nEqn5 :=\nInt(nu_integrand,nu)=Int(xx_in tegrand,xx)+_C;\neqn5 :=\nint(nu_integrand,nu)=int(xx_integrand,xx)+_C ;\neqn6 :=\nsubs(nu = yy(xx)/xx,eqn5);\nRETURN( [eqn,yy(xx)=xx*nu(xx), eqn2,eqn3,eqn4,Eqn5,eqn5,eqn6]);\n\nelse\nEqn5 :=Int(subs(nu=eta,nu_in tegrand),eta=y_0/x_0..nu(xx))=Int(subs(xx=xi,xx_integrand),xi=x_0..xx) ;\neqn5 := int(subs(nu=eta,nu_integrand),eta=y_0/x_0..nu(xx))=int(subs (xx=xi,xx_integrand),xi=x_0..xx);\neqn6 := subs(nu(xx) = yy(xx)/xx,eqn 5);\nRETURN([eqn,yy(xx)=xx*nu(xx),eqn2,eqn3,eqn4,Eqn5,eqn5,eqn6]);\nfi :\n\nend:" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}{SECT 0 {PARA 4 "" 0 " " {TEXT 360 14 "Description of" }{TEXT -1 2 " " }{TEXT 281 15 "homoge neous_ode" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 15 "homogeneous_ode" }{TEXT 30 76 " - Exhibit steps for solving a firs t order homogeneous differential equation" }}{PARA 4 "" 0 "usage" {TEXT -1 18 "Calling Sequences:" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 282 47 "homogeneous_ode(ode)\n homogeneous_ode(ode, ic)" }} {PARA 4 "" 0 "" {TEXT -1 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 23 58 "ode - an equation of the form diff(y(x),x) \+ = F(x,y(x)) " }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 23 65 "ic \+ - an equation of the form y(a) = c (the initial condition)" }}{PARA 0 "" 0 "" {TEXT 23 1 "\n" }{TEXT 283 12 "Description:" }}{PARA 15 "" 0 "" {TEXT -1 9 "The call " }{TEXT 284 42 " homogeneous_ode(diff(y(x), x) = F(x,y(x)))" }{TEXT -1 22 " returns a list with\n" }{TEXT 285 1 " 7" }{TEXT -1 29 " entries. The first entry is " }{TEXT 326 24 "diff(y( x),x) = F(x,y(x))" }{TEXT -1 128 " and the last entry is the solution \+ of this differential equation (in implicit equation form). Further det ails will be provided." }}{PARA 15 "" 0 "" {TEXT -1 67 "The required f orm of the equation passed as the first argument of " }{TEXT 297 15 " homogeneous_ode" }{TEXT -1 80 " is strictly enforced. In particular, \+ the left hand side of the first equation " }{TEXT 287 4 "must" }{TEXT -1 17 " be of the form " }{TEXT 286 12 "diff(y(x),x)" }{TEXT -1 60 " \+ and nothing else. For example, the differential equations " }{TEXT 288 38 "\n diff(y(x),x)+x/y(x)=y(x)/x" }{TEXT -1 2 ", " } {TEXT 289 32 " \n x*diff(y(x),x)=y(x)" }{TEXT -1 7 ", \nand \+ " }{TEXT 290 28 "\n 1 = diff(y(x),x)" }{TEXT -1 139 ",\nwhil e perfectly valid as homogeneous differential equations, nevertheless \+ result in error messages when passed as the first argument of " } {TEXT 298 15 "homogeneous_ode" }{TEXT -1 2 ". " }}{PARA 15 "" 0 "" {TEXT -1 4 "If " }{TEXT 291 1 "x" }{TEXT -1 6 " and " }{TEXT 292 2 " y" }{TEXT -1 108 " are respectively the independent and dependent va riables of the differential equation, then the expression" }{TEXT 294 2 "y " }{TEXT -1 73 "cannot appear on either the left or right side of the first argument of " }{TEXT 299 15 "homogeneous_ode" }{TEXT -1 20 ". It must appear as " }{TEXT 293 4 "y(x)" }{TEXT -1 8 ". Thus, " } {TEXT 295 21 "diff(y(x),x) = x/y(x)" }{TEXT -1 32 " is a valid first \+ argument but " }{TEXT 296 19 " diff(y(x),x) = x/y" }{TEXT -1 9 " is n ot." }}{PARA 15 "" 0 "" {TEXT -1 9 "The call " }{TEXT 300 42 " homogen eous_ode(diff(y(x),x) = F(x,y(x)))" }{TEXT -1 97 " results in a check for homogeneity. To be specific, an attempt is made to verify the ide ntity " }{TEXT 301 17 "F(t*u,t*v)=F(u,v)" }{TEXT -1 57 " is examined . If this identity cannot be verified, then " }{TEXT 302 41 "homogeneo us_ode(diff(y(x),x) = F(x,y(x)))" }{TEXT -1 36 " returns a string with that message." }}{PARA 15 "" 0 "" {TEXT -1 40 "If the first order dif ferential equation" }{TEXT 303 4 " ode" }{TEXT -1 18 " is of the form " }{TEXT 309 24 "diff(y(x),x) = F(x,y(x))" }{TEXT -1 50 " and if it passes the test for homogeneity, then " }{TEXT 304 20 "homogeneous_od e(ode)" }{TEXT -1 46 " implements the change of variable\n\n \+ " }{XPPEDIT 18 0 "y(x) = x*nu(x);" "/-%\"yG6#%\"xG*&F&\"\"\"-%#nuG6#F& F(" }{TEXT -1 56 ". \n\nThis equation is the second entry of the retur n of " }{TEXT 306 20 "homogeneous_ode(ode)" }{TEXT -1 36 ". The third entry of the return of " }{TEXT 307 20 "homogeneous_ode(ode)" } {TEXT -1 179 "is the differential equation that results when the afore mentioned change of variable is made (but prior to any further algebra ic manipulation). The fourth entry of the return of " }{TEXT 308 20 " homogeneous_ode(ode)" }{TEXT -1 27 "is obtained by isolating " } {XPPEDIT 18 0 "diff(nu(x),x);" "-%%diffG6$-%#nuG6#%\"xGF(" }{TEXT -1 74 " (without further algebraic manipulation). The fifth entry retur ned by " }{TEXT 310 21 "homogeneous_ode(ode) " }{TEXT -1 75 "is obtai ned by simplifying the right side of the differential equation in " } {XPPEDIT 18 0 "nu(x);" "-%#nuG6#%\"xG" }{TEXT -1 34 " so that it appe ars clearly as " }{XPPEDIT 18 0 "diff(nu(x),x) = G(x)*H(nu(x));" "/- %%diffG6$-%#nuG6#%\"xGF)*&-%\"GG6#F)\"\"\"-%\"HG6#-F'6#F)F." }{TEXT -1 2 " ." }}{PARA 15 "" 0 "" {TEXT -1 35 "The final two entries return ed by " }{TEXT 311 15 "homogeneous_ode" }{TEXT -1 58 " depend on whe ther it is called with one argument or two." }}{PARA 15 "" 0 "" {TEXT -1 90 "Continuing with the notation used in a previous bullet item, th e sixth entry returned by " }{TEXT 312 20 "homogeneous_ode(ode)" } {TEXT -1 9 " is " }{XPPEDIT 18 0 "Int(1/H(nu),nu) = Int(G(x),x)+_ C;" "/-%$IntG6$*&\"\"\"F'-%\"HG6#%#nuG!\"\"F+,&-F$6$-%\"GG6#%\"xGF3F'% #_CGF'" }{TEXT -1 51 " . This is also the sixth entry of the return o f " }{TEXT 313 27 "homogeneous_ode(ode,y(0)=c)" }{TEXT -1 9 ". If \+ " }{XPPEDIT 18 0 "a <> 0;" "0%\"aG\"\"!" }{TEXT -1 8 ", then " } {TEXT 314 27 "homogeneous_ode(ode,y(a)=c)" }{TEXT -1 11 " returns " }{XPPEDIT 18 0 "Int(1/H(eta),eta = c/a .. nu(x)) = Int(G(xi),xi = a .. x);" "/-%$IntG6$*&\"\"\"F'-%\"HG6#%$etaG!\"\"/F+;*&%\"cGF'%\"aGF,-%#n uG6#%\"xG-F$6$-%\"GG6#%#xiG/F;;F1F5" }{TEXT -1 23 " as its sixth en try." }}{PARA 15 "" 0 "" {TEXT -1 21 "The final entry of " }{TEXT 315 20 "homogeneous_ode(ode)" }{TEXT -1 4 " or " }{TEXT 317 27 "homoge neous_ode(ode,y(0)=c)" }{TEXT -1 48 " is an equation that provides th e solution to " }{TEXT 316 3 "ode" }{TEXT -1 57 " in implicit form i nvolving a constant of integration, " }{TEXT 318 2 "_C" }{TEXT -1 8 " . If " }{XPPEDIT 18 0 "a <> 0;" "0%\"aG\"\"!" }{TEXT -1 8 ", then \+ " }{TEXT 319 27 "homogeneous_ode(ode,y(a)=c)" }{TEXT -1 40 " solves fo r the constant of integration." }}{PARA 15 "" 0 "" {TEXT -1 129 "No at tempt is made to verify the correctness of the solution. It is recomme nded that the user test for correctness with the call " }{TEXT 320 36 "odetest(homogeneous_ode(ode)[7],ode)" }{TEXT -1 34 ". The result of t his call will be " }{TEXT 321 1 "0" }{TEXT -1 27 " if the solution fo und by " }{TEXT 322 15 "homogeneous_ode" }{TEXT -1 12 " is correct." } }{PARA 15 "" 0 "" {TEXT -1 63 "Because nu is used as the change of var iable, the arguments of " }{TEXT 323 15 "homogeneous_ode" }{TEXT -1 22 " should be free of nu." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 305 8 "Example:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 324 14 "First example:" }{TEXT -1 1 "\n" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "diff_eq := diff(y(x),x) = x* y(x)/(x^2 + y(x)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(diff_eqG/-% %diffG6$-%\"yG6#%\"xGF,*(F,\"\"\"F)F.,&*$F,\"\"#F.*$F)F1F.!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "homogeneous_ode(diff_eq);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#7*/-%%diffG6$-%\"yG6#%\"xGF+*(F+\"\" \"F(F-,&*$F+\"\"#F-*$F(F0F-!\"\"/F(*&F+F--%#nuGF*F-/,&F5F-*&F+F--F&6$F 5F+F-F-*(F+F0F5F-,&F/F-*&F+F0F5F0F-F2/F:,$*(F5\"\"$F+F2,&F-F-*$F5F0F-F 2F2F?/-%$IntG6$*&F6!\"$,&F-F-*$F6F0F-F-F6,&-FG6$,$*$F+F2F2F+F-%#_CGF-/ ,&-%#lnG6#F6F-*$F6!\"##F2F0,&-FVF*F2FRF-/,&-FV6#*&F(F-F+F2F-*&F(FYF+F0 FZFen" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT 325 15 "Second Example:" }{TEXT -1 1 "\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "ode := diff(y(x),x) = 1+(y(x)/x)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG/-%%diffG6$-%\"yG6#%\"xGF,,&\"\"\"F.*&F)\"\"# F,!\"#F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ic := y(1) = -1 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#icG/-%\"yG6#\"\"\"!\"\"" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "homogeneous_ode(ode,ic);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7*/-%% diffG6$-%\"yG6#%\"xGF+,&\"\"\"F-*&F(\"\"#F+!\"#F-/F(*&F+F--%#nuGF*F-/, &F3F-*&F+F--F&6$F3F+F-F-,&F-F-*$F3F/F-/F8*&,(F3!\"\"F-F-F;F-F-F+F?F " 0 "" {MPLTEXT 1 0 149 "soln_plot := implicitplot(2/3*arctan(1/3*3^(1/2)*(2* y(x)/x-1))*3^(1/2)+2/9*Pi*3^(1/2) = ln(x), x = 0.1..2, y = -3..1/2, co lor = maroon, thickness=2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "df_plot := dfieldplot(ode, y(x), x = 0.1..2, y = -3..1/2, color = \+ gold):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display(\{soln_pl ot,df_plot\});" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6^p7$7$$\"1i \"z5f$=qm!#;$!\"$\"\"!7$$\"1^*fhngIq'F*$!12jw3QcIH!#:7$7$$\"1X)QC_!oRn F*$!1++++++gGF3F.7$F57$$\"1$GA=-?%pnF*$!1Pnv)*yy-GF37$7$$\"1;G;r8a;oF* $!1++++++?FF3F;7$FA7$$\"1;uK+-qToF*$!1m8[oE5wEF37$7$$\"1aiaKf%>!pF*$!1 ++++++!e#F3FG7$FM7$$\"1W=wq$*e?pF*$!13x3%)[j]DF37$7$$\"1:o2AlK(*pF*$!1 ++++++SCF3FS7$FY7$$\"1j!Hc!=&o+(F*$!1!)ehK`_ECF37$7$$\"1++++++!3(F*$!1 7xA>>oJBF3Fin7$F_o7$$\"1qlX$psO5(F*$!1Y4Kf2O/BF37$7$$\"1g\\Xk%[x5(F*$! 1*************H#F3Feo7$7$$\"1f\\Xk%[x5(F*F^p7$$\"1\"zJ$Q&y&=sF*$!1r@[D w_&=#F37$7$$\"1mpk6v>XsF*$!1************f@F3Fdp7$Fjp7$$\"1M2-=_^WtF*$! 1M,`([E(o?F37$7$$\"19Jn)G<:S(F*$!1************>?F3F`q7$Ffq7$$\"1#>M(3P b#[(F*$!1)Hc0jaT&>F37$7$$\"1/C\"z`i/e(F*$!1************z=F3F\\r7$7$$\" 1-C\"z`i/e(F*Fer7$$\"1M$es)>sLwF*$!1#[0(=9+U=F37$7$$\"1\"H+$Qar'y(F*$! 1************R(p;Z3 C$3$Hn1#)F*$!1#RuN,Xv_\"F37$7$$\"1DjR%Q8]U()F*$!1**** ********>8F3Fjv7$F`w7$$\"13GKh?@y*)F*$!1`_(Gkq'\\7F37$7$$\"1`z:Q1w=#*F *$!1)***********z6F3Ffw7$F\\x7$$\"1qF])f@zF*F*$!1N5Y%H!)[;\"F37$7$$\"1 )***********f$*F*$!1b:PaoKW6F3Fbx7$7$$\"1************f$*F*F[y7$$\"18** em]+6'*F*$!1cWUvxB'3\"F37$7$$\"1!*4OV#GK\")*F*$!1)***********R5F3Fay7$ Fgy7$$\"1\"H*Ra_eg**F*$!1%R5e7M1,\"F37$7$$\"1++++++75F3$!1b+tBSY)y*F*F ]z7$Fcz7$$\"1!)=`!zoL.\"F3$!1?41:cj$R*F*7$7$$\"1p)>&ox]a5F3$!1%)****** *******)F*Fiz7$7$F`[l$!1#)*************)F*7$$\"1r'pQg&Rs5F3$!1#>*f(f]D r)F*7$7$$\"1++++++)3\"F3$!1)*o!o9^cX)F*Fh[l7$7$F_\\l$!1(*o!o9^cX)F*7$$ \"1\"F3$!1-L09R9boF*7$7$$\"1++++++S7F3$!1![f(G>N-jF *F_^l7$Fe^l7$$\"1yj\"oJ-LC\"F3$!1G1)=:K3E'F*7$7$$\"1xjiOs(yC\"F3$!1$)* **********>'F*F[_l7$7$Fb_l$!1#)***********>'F*7$$\"1QpZ#oF**G\"F3$!19/ om/s>dF*7$7$$\"1++++++;8F3$!1]L-fP<)R&F*Fj_l7$F``l7$$\"1'f02=yhL\"F3$! 1wsyGLqr^F*7$7$$\"1NrXiz$oO\"F3$!1#)***********z%F*Ff`l7$F\\al7$$\"1F# \\Q+;HQ\"F3$!1O:!)GKmKYF*7$7$$\"1++++++#R\"F3$!1$f*z\"eY$GXF*Fbal7$Fha l7$$\"1.!*\\Q0DJ9F3$!1Gz]Ni.BTF*7$7$$\"1++++++o9F3$!1Z*=)4(f^q$F*F^bl7 $Fdbl7$$\"1bz32.ky9F3$!1kL)ol0gf$F*7$7$$\"1Mqu$eFg\\\"F3$!1#)********* **R$F*Fjbl7$F`cl7$$\"1)pZj/vt_\"F3$!1lLx`3v$4$F*7$7$$\"1++++++W:F3$!1( Q'pd$G?\"HF*Ffcl7$F\\dl7$$\"15=6x[Ow:F3$!147p/^>'f#F*7$7$$\"1++++++?;F 3$!1BH]u&)e@@F*Fbdl7$7$Fidl$!1AH]u&)e@@F*7$$\"1HBu9gJC;F3$!1)4FZ`0&z?F *7$7$$\"1&>q-Ie;j\"F3$!1#)************>F*Fael7$Fgel7$$\"1)>Dv!R7u;F3$! 1r$[\"\\$>qf\"F*7$7$$\"1++++++'p\"F3$!1rFI>l@j8F*F]fl7$Fcfl7$$\"1YGPF) GLs\"F3$!1=XRndU.6F*7$7$$\"127lH>dq F3$\"1&=++++++)FdglF^il7$Fdil7$$\"1V&RN,&[>>F3$\"1u)*=K!3<$))Fdgl7$7$$ \"1,+++++C>F3$\"15q>qX#\\J*FdglFjil7$F`jl7$$\"1Mtf&H[%p>F3$\"1qfyaXzi8 F*7$7$$\"\"#F-$\"1?xij!)z)o\"F*Ffjl-%'COLOURG6&%$RGBG$\")viob!\")$\")! \\DP\"Fg[m$\")%yg>%Fg[m-%*THICKNESSG6#F^[m-F$6]dl7%7$$\"+iux*)**!#6$!+ r]5#4$!\"*7$$\"+aA-,5!#5$!+H\\*y!HFh\\m7$$\"+k')zb()Fe\\m$!+<0tZHFh\\m 7%7$$\"+\"oCf*>F\\]m$!+/A5#4$Fh\\m7$$\"+>`2/?F\\]m$!+'z(*y!HFh\\m7$$\" +1[Jx=F\\]m$!+T:fZHFh\\m7%7$$\"+$=#)3*HF\\]m$!+[**3#4$Fh\\m7$$\"+!)GF\\]m$!+qiOZHFh\\m7%7$$\"+m+#R)RF\\]m$ !+@w0#4$Fh\\m7$$\"+M*zg,%F\\]m$!+zB%z!HFh\\m7$$\"+w<=%)QF\\]m$!+vR1ZHF h\\m7%7$$\"+![P^(\\F\\]m$!+C8*>4$Fh\\m7$$\"+?D'[-&F\\]m$!+w'3!3HFh\\m7 $$\"+l8D*)[F\\]m$!+.rpYHFh\\m7%7$$\"+yMmkfF\\]m$!+d\\(=4$Fh\\m7$$\"+Al LNgF\\]m$!+V]73HFh\\m7$$\"+*)F\\]m$!+&y3\\%HFh\\m7%7$$ \"+&y=%4**F\\]m$!+:7e!4$Fh\\m7$$\"+@\"e!45Fh\\m$!+&y=%4HFh\\m7$$\"+XnU G**F\\]m$!+)4qW%HFh\\m7%7$$\"+fcL*3\"Fh\\m$!+()e)**3$Fh\\m7$$\"+TVm56F h\\m$!+8T,5HFh\\m7$$\"+vT$Q4\"Fh\\m$!+Nz1WHFh\\m7%7$$\"+iqo(=\"Fh\\m$! ++)o#*3$Fh\\m7$$\"+QHJ77Fh\\m$!++7t5HFh\\m7$$\"+Gi'[>\"Fh\\m$!+#H:P%HF h\\m7%7$$\"+'p>gG\"Fh\\m$!+F;V)3$Fh\\m7$$\"+/.)RJ\"Fh\\m$!+t$o:\"HFh\\ m7$$\"+?_#fH\"Fh\\m$!+$4AM%HFh\\m7%7$$\"+WcN%Q\"Fh\\m$!+(o![(3$Fh\\m7$ $\"+cVk:9Fh\\m$!+8$>D\"HFh\\m7$$\"+sx*pR\"Fh\\m$!+C\\>VHFh\\m7%7$$\"+K Zr#[\"Fh\\m$!+SjU'3$Fh\\m7$$\"+o_G<:Fh\\m$!+gOd8HFh\\m7$$\"+Q72)\\\"Fh \\m$!+Uq.VHFh\\m7%7$$\"++S6\"e\"Fh\\m$!+$4#G&3$Fh\\m7$$\"++g))=;Fh\\m$ !+2zr9HFh\\m7$$\"+CT8*f\"Fh\\m$!+P'[H%HFh\\m7%7$$\"+\"Rn&z;Fh\\m$!+rN1 %3$Fh\\m7$$\"+4EV?#=Fh\\m$!+QD@Fh \\m$!+Q%H&=HFh\\m7$$\"+#Qn@!>Fh\\m$!+jh1VHFh\\m7%7$$\"+G\\Mv>Fh\\m$!+% )*G,3$Fh\\m7$$\"+s]lC?Fh\\m$!+;5()>HFh\\m7$$\"+lW5.?Fh\\m$!+uN@VHFh\\m 7%7$$\"+HzR))**Fe\\m$!+*[%*y!HFh\\m7$$\"+2-;,5F\\]m$!+fWoBFFh\\m7$$\"+ #f\"ec()Fe\\m$!+qO^jFFh\\m7%7$$\"+GoP&*>F\\]m$!++3*y!HFh\\m7$$\"+sJi/? F\\]m$!+[\")oBFFh\\m7$$\"+Cmix=F\\]m$!+$GcLw#Fh\\m7%7$$\"+$\\k'*)HF\\] m$!+d](y!HFh\\m7$$\"+2bL5IF\\]m$!+\"*QqBFFh\\m7$$\"+5o)3)GF\\]m$!+T@5j FFh\\m7%7$$\"+nHz\")RF\\]m$!+_O$y!HFh\\m7$$\"+Lq?=SF\\]m$!+'HXPs#Fh\\m 7$$\"+egS&)QF\\]m$!+7JwiFFh\\m7%7$$\"+?/*=(\\F\\]m$!+o!\\x!HFh\\m7$$\" +!e4\"G]F\\]m$!+!))HQs#Fh\\m7$$\"+oa8\"*[F\\]m$!+K]NiFFh\\m7%7$$\"+\\N 7gfF\\]m$!+^8g2HFh\\m7$$\"+^k()RgF\\]m$!+(fxRs#Fh\\m7$$\"+3w+)*eF\\]m$ !+!*o*=w#Fh\\m7%7$$\"+)e'pYpF\\]m$!+`)pt!HFh\\m7$$\"+7MI`qF\\]m$!+&44U s#Fh\\m7$$\"+,Z$f!pF\\]m$!++)49w#Fh\\m7%7$$\"+%)z%=$zF\\]m$!+C^.2HFh\\ m7$$\"+;?:o!)F\\]m$!+CQaCFFh\\m7$$\"+Yz![\"zF\\]m$!+qd\"4w#Fh\\m7%7$$ \"+_U%e\"*)F\\]m$!+]2e1HFh\\m7$$\"+[d:%3*F\\]m$!+)>)*\\s#Fh\\m7$$\"+3& )\\C*)F\\]m$!+!QO/w#Fh\\m7%7$$\"+05(*)*)*F\\]m$!+L\\*f!HFh\\m7$$\"++H5 55Fh\\m$!+:SeDFFh\\m7$$\"+n/'[$**F\\]m$!+u9**fFFh\\m7%7$$\"+u@:)3\"Fh \\m$!+.;F0HFh\\m7$$\"+Ey%=6\"Fh\\m$!+XtIEFFh\\m7$$\"+kNd%4\"Fh\\m$!+3! )ffFFh\\m7%7$$\"+Z&yj=\"Fh\\m$!+O4T/HFh\\m7$$\"+`9i87Fh\\m$!+7!ors#Fh \\m7$$\"+#*fp&>\"Fh\\m$!+$>p#fFFh\\m7%7$$\"+cMg%G\"Fh\\m$!+E#>M!HFh\\m 7$$\"+WlR:8Fh\\m$!+A(f\"GFFh\\m7$$\"+Oq$oH\"Fh\\m$!+/S,fFFh\\m7%7$$\"+ A9&GQ\"Fh\\m$!+l\"3B!HFh\\m7$$\"+y&[rT\"Fh\\m$!+$yq#HFFh\\m7$$\"+/7)zR \"Fh\\m$!+/r$)eFFh\\m7%7$$\"+iM9\"[\"Fh\\m$!+(o$4,HFh\\m7$$\"+Ql&)=:Fh \\m$!+h_[IFFh\\m7$$\"+Fh\\m$!++&))ft#Fh\\m7$$\"+?cK.>Fh\\m$!+`b/fFF h\\m7%7$$\"+;Nst>Fh\\m$!+a.:%*GFh\\m7$$\"+%[wi-#Fh\\m$!+%fGut#Fh\\m7$$ \"+UPE/?Fh\\m$!+Q)e#fFFh\\m7%7$$\"+C#>n)**Fe\\m$!+')QoBFFh\\m7$$\"+y!G 8+\"F\\]m$!+5SZRDFh\\m7$$\"+XW`d()Fe\\m$!+daHzDFh\\m7%7$$\"+[3r%*>F\\] m$!+e!zOs#Fh\\m7$$\"+_\"*G0?F\\]m$!+Q)y%RDFh\\m7$$\"+we+y=F\\]m$!+wd6z DFh\\m7%7$$\"+lo=))HF\\]m$!+,&eOs#Fh\\m7$$\"+NJ\"=,$F\\]m$!+&R*\\RDFh \\m7$$\"+!zK<)GF\\]m$!+&)p#)yDFh\\m7%7$$\"+C&=#zRF\\]m$!+AYgBFFh\\m7$$ \"+w9y?SF\\]m$!+uKbRDFh\\m7$$\"+Z3*o)QF\\]m$!+=XWyDFh\\m7%7$$\"+*Ruz' \\F\\]m$!+$3&\\BFFh\\m7$$\"+,c-K]F\\]m$!+8GmRDFh\\m7$$\"+#y9M*[F\\]m$! +/)))zd#Fh\\m7%7$$\"+.MnafF\\]m$!+q\\IBFFh\\m7$$\"+(fE`/'F\\]m$!+EH&)R DFh\\m7$$\"+*G97!fF\\]m$!+\\S[xDFh\\m7%7$$\"+LCeRpF\\]m$!+=$4Is#Fh\\m7 $$\"+nvTgqF\\]m$!+y&[,a#Fh\\m7$$\"+>><5pF\\]m$!+-n&pd#Fh\\m7%7$$\"+D-, BzF\\]m$!+ndeAFFh\\m7$$\"+v(*)p2)F\\]m$!+H@dSDFh\\m7$$\"+qH9?zF\\]m$!+ cOVwDFh\\m7%7$$\"+%*oH0*)F\\]m$!+(*p,AFFh\\m7$$\"+1Jq%4*F\\]m$!+**39TD Fh\\m7$$\"+1\"e4$*)F\\]m$!+'RSfd#Fh\\m7%7$$\"+)e*z'))*F\\]m$!+EEH@FFh \\m7$$\"+T+K65Fh\\m$!+q_'=a#Fh\\m7$$\"+;*GC%**F\\]m$!+b#*\\vDFh\\m7%7$ $\"+jvy'3\"Fh\\m$!+*G5/s#Fh\\m7$$\"+PC@86Fh\\m$!+2wuUDFh\\m7$$\"+-cV&4 \"Fh\\m$!+J!G^d#Fh\\m7%7$$\"+?l)[=\"Fh\\m$!+bdP>FFh\\m7$$\"+![8^@\"Fh \\m$!+T@yVDFh\\m7$$\"+qQl'>\"Fh\\m$!+=\"R[d#Fh\\m7%7$$\"+'e2IG\"Fh\\m$ !+J@?=FFh\\m7$$\"+9C*pJ\"Fh\\m$!+ld&\\a#Fh\\m7$$\"+z%yyH\"Fh\\m$!+]#RY d#Fh\\m7%7$$\"+tq<\"Q\"Fh\\m$!+Y$3pr#Fh\\m7$$\"+FH#)=9Fh\\m$!+]&\\ia#F h\\m7$$\"+U>4*R\"Fh\\m$!+5)HXd#Fh\\m7%7$$\"+\\hTz9Fh\\m$!+?s^:FFh\\m7$ $\"+^Qe?:Fh\\m$!+w1kZDFh\\m7$$\"+f\"z-]\"Fh\\m$!+4w]uDFh\\m7%7$$\"+L1u x:Fh\\m$!+]M09FFh\\m7$$\"+n$fAi\"Fh\\m$!+YW5\\DFh\\m7$$\"+5yU,;Fh\\m$! +GfcuDFh\\m7%7$$\"+>7;w;Fh\\m$!+!yTDr#Fh\\m7$$\"+\"yQQs\"Fh\\m$!+;hh]D Fh\\m7$$\"+t%GDq\"Fh\\m$!+lcpuDFh\\m7%7$$\"+ASouFh\\m$!+PAp`DFh\\m7$$\"+;=c/>Fh\\m$!+At7 vDFh\\m7%7$$\"+XA/s>Fh\\m$!+?+%zq#Fh\\m7$$\"+bx&z-#Fh\\m$!+wy@bDFh\\m7 $$\"+.%)[0?Fh\\m$!+3zSvDFh\\m7%7$$\"+.#[Y)**Fe\\m$!+^KZRDFh\\m7$$\"+!= N:+\"F\\]m$!+$fj_N#Fh\\m7$$\"+p,re()Fe\\m$!+ba2&R#Fh\\m7%7$$\"+h-*Q*>F \\]m$!+4oYRDFh\\m7$$\"+R(4h+#F\\]m$!+N+FbBFh\\m7$$\"+xMZy=F\\]m$!+P%o[ R#Fh\\m7%7$$\"+%>qj)HF\\]m$!+e%R%RDFh\\m7$$\"+1)HO,$F\\]m$!+'Q(HbBFh\\ m7$$\"+zVx#)GF\\]m$!+Ew`%R#Fh\\m7%7$$\"+?O1wRF\\]m$!+\"3o$RDFh\\m7$$\" +!QOR-%F\\]m$!+j(o`N#Fh\\m7$$\"+V\\r))QF\\]m$!+^M5%R#Fh\\m7%7$$\"+mm>j \\F\\]m$!+OQARDFh\\m7$$\"+ML!o.&F\\]m$!+3I^bBFh\\m7$$\"+/h?'*[F\\]m$!+ zEf$R#Fh\\m7%7$$\"+^@1[fF\\]m$!+Aa(*QDFh\\m7$$\"+\\y$>0'F\\]m$!+A9wbBF h\\m7$$\"+:V70fF\\]m$!+Ul.$R#Fh\\m7%7$$\"+kW,JpF\\]m$!+9GfQDFh\\m7$$\" +Ob)*oqF\\]m$!+IS9cBFh\\m7$$\"+!R4`\"pF\\]m$!+&QoCR#Fh\\m7%7$$\"+m\"eC \"zF\\]m$!+()40QDFh\\m7$$\"+M=a(3)F\\]m$!+deocBFh\\m7$$\"+8fcEzF\\]m$! +F5#>R#Fh\\m7%7$$\"+.,$G*))F\\]m$!+\"3Lt`#Fh\\m7$$\"+(*)pr5*F\\]m$!+jP SdBFh\\m7$$\"+w!p'Q*)F\\]m$!+ZTU\"R#Fh\\m7%7$$\"+8lds)*F\\]m$!+)\\Kk`# Fh\\m7$$\"+\\Bu75Fh\\m$!+YVIeBFh\\m7$$\"+F[P^**F\\]m$!+N?+\"R#Fh\\m7%7 $$\"+6G@&3\"Fh\\m$!+oNNNDFh\\m7$$\"+*=(y96Fh\\m$!+wKQfBFh\\m7$$\"+2LW' 4\"Fh\\m$!+s?n!R#Fh\\m7%7$$\"+&o(=$=\"Fh\\m$!+s26MDFh\\m7$$\"+:B\"o@\" Fh\\m$!+sgigBFh\\m7$$\"+$>gx>\"Fh\\m$!+)4W/R#Fh\\m7%7$$\"+td@\"G\"Fh\\ m$!+ansKDFh\\m7$$\"+FUy=8Fh\\m$!+!45?O#Fh\\m7$$\"+tg1*H\"Fh\\m$!+,2K!R #Fh\\m7%7$$\"+yPKz8Fh\\m$!+@'H7`#Fh\\m7$$\"+Ain?9Fh\\m$!+Bs]jBFh\\m7$$ \"+#*>M+9Fh\\m$!+V#)H!R#Fh\\m7%7$$\"+l7`x9Fh\\m$!+\\+lHDFh\\m7$$\"+N(o C_\"Fh\\m$!+&z'3lBFh\\m7$$\"+&ps:]\"Fh\\m$!+T$o.R#Fh\\m7%7$$\"+$*4&ed \"Fh\\m$!+u'=!GDFh\\m7$$\"+2!\\Ti\"Fh\\m$!+q\"=nO#Fh\\m7$$\"+*yYFg\"Fh \\m$!++&>0R#Fh\\m7%7$$\"+8(*Gu;Fh\\m$!+bSOEDFh\\m7$$\"+(G5ds\"Fh\\m$!+ *ys$oBFh\\m7$$\"+ql&Qq\"Fh\\m$!+Q'Q2R#Fh\\m7%7$$\"+S#\\Gx\"Fh\\m$!+=8r CDFh\\m7$$\"+g2:F=Fh\\m$!+Eb-qBFh\\m7$$\"++w*[!=Fh\\m$!+VB,\"R#Fh\\m7% 7$$\"+$fF:(=Fh\\m$!+f93BDFh\\m7$$\"+2CZG>Fh\\m$!+&Qb;P#Fh\\m7$$\"+_\"o e!>Fh\\m$!+*zF8R#Fh\\m7%7$$\"+q+Kq>Fh\\m$!+q6\\@DFh\\m7$$\"+I*z'H?Fh\\ m$!+ucCtBFh\\m7$$\"+F'on+#Fh\\m$!+xLn\"R#Fh\\m7%7$$\"+jC0#)**Fe\\m$!+m DEbBFh\\m7$$\"+aZz,5F\\]m$!+EK0r@Fh\\m7$$\"+#3%=g()Fe\\m$!+lI&3@#Fh\\m 7%7$$\"+!RjG*>F\\]m$!+xPDbBFh\\m7$$\"+5m82?F\\]m$!+:?1r@Fh\\m7$$\"+,\" f!z=F\\]m$!+T?h5AFh\\m7%7$$\"+$4.T)HF\\]m$!+&f;_N#Fh\\m7$$\"+2p*e,$F\\ ]m$!+(>*4r@Fh\\m7$$\"+Ql2%)GF\\]m$!+*oH-@#Fh\\m7%7$$\"+0E9sRF\\]m$!+%4 ?^N#Fh\\m7$$\"+&Rdy-%F\\]m$!+)p&>r@Fh\\m7$$\"+\\*))4*QF\\]m$!+#fL(4AFh \\m7%7$$\"+V@Hd\\F\\]m$!+^l#\\N#Fh\\m7$$\"+dyqU]F\\]m$!+T#*Qr@Fh\\m7$$ \"+Q;n**[F\\]m$!+D%f\"4AFh\\m7%7$$\"+v9&*RfF\\]m$!+;lfaBFh\\m7$$\"+D&[ +1'F\\]m$!+w#><<#Fh\\m7$$\"+\"[^*4fF\\]m$!+nza3AFh\\m7%7$$\"+m!*f?pF\\ ]m$!+(Q%4aBFh\\m7$$\"+M4SzqF\\]m$!+09As@Fh\\m7$$\"+7bg@pF\\]m$!+R9%z?# Fh\\m7%7$$\"+`3x**yF\\]m$!+GOR`BFh\\m7$$\"+Z\"H-5)F\\]m$!+k@#H<#Fh\\m7 $$\"+ueOMzF\\]m$!+m&zt?#Fh\\m7%7$$\"+g&H!y))F\\]m$!+p1[_BFh\\m7$$\"+S/ (>7*F\\]m$!+B^$Q<#Fh\\m7$$\"+F>$z%*)F\\]m$!+ef*o?#Fh\\m7%7$$\"+'eGf&)* F\\]m$!+RnN^BFh\\m7$$\"+TrS95Fh\\m$!+`!f\\<#Fh\\m7$$\"+G#))>'**F\\]m$! +0a^1AFh\\m7%7$$\"+[wR$3\"Fh\\m$!+nt.]BFh\\m7$$\"+_Bg;6Fh\\m$!+D%yi<#F h\\m7$$\"+PDi(4\"Fh\\m$!+?DD1AFh\\m7%7$$\"+83E\"=\"Fh\\m$!+:)\\&[BFh\\ m7$$\"+(=R(=7Fh\\m$!+xfwx@Fh\\m7$$\"+yf.*>\"Fh\\m$!+u=61AFh\\m7%7$$\"+ %o;#z7Fh\\m$!+;#HpM#Fh\\m7$$\"+;Ly?8Fh\\m$!+wlQz@Fh\\m7$$\"+6\\T+8Fh\\ m$!+e$*31AFh\\m7%7$$\"+e)*Gx8Fh\\m$!+=V@XBFh\\m7$$\"+U,rA9Fh\\m$!+u95 \"=#Fh\\m7$$\"+L,u,9Fh\\m$!+HV<1AFh\\m7%7$$\"+'o&\\v9Fh\\m$!+`OWVBFh\\ m7$$\"+9V]C:Fh\\m$!+R@(G=#Fh\\m7$$\"+6x*H]\"Fh\\m$!+5?N1AFh\\m7%7$$\"+ 3:%Qd\"Fh\\m$!+@ElTBFh\\m7$$\"+#\\ehi\"Fh\\m$!+rJm%=#Fh\\m7$$\"+x'yTg \"Fh\\m$!+5dg1AFh\\m7%7$$\"+a#GBn\"Fh\\m$!+s;()RBFh\\m7$$\"+Y)=#Fh\\m7$$\"+1cH1=Fh\\m$!+7\\F2AFh \\m7%7$$\"+%41(p=Fh\\m$!+FHVOBFh\\m7$$\"+1RHI>Fh\\m$!+lG))*=#Fh\\m7$$ \"+\"zJs!>Fh\\m$!+V2m2AFh\\m7%7$$\"+?7eo>Fh\\m$!+5v![L#Fh\\m7$$\"+!y=9 .#Fh\\m$!+#G3:>#Fh\\m7$$\"+t,43?Fh\\m$!++V13AFh\\m7%7$$\"+)pQ(y**Fe\\m $!++=0r@Fh\\m7$$\"+Ih7-5F\\]m$!+SH%o)>Fh\\m7$$\"+)=m?w)Fe\\m$!+9uiE?Fh \\m7%7$$\"+)4b:*>F\\]m$!+&\\R5<#Fh\\m7$$\"+-\\W3?F\\]m$!+X_&o)>Fh\\m7$ $\"+#)f!)z=F\\]m$!+&RVj-#Fh\\m7%7$$\"+t[A\")HF\\]m$!+vw)4<#Fh\\m7$$\"+ F^x=IF\\]m$!+lq!p)>Fh\\m7$$\"+;Mt&)GF\\]m$!+Uq*e-#Fh\\m7%7$$\"+n4>nRF \\]m$!+HT&3<#Fh\\m7$$\"+L!4G.%F\\]m$!+61/()>Fh\\m7$$\"+.<(Q*QF\\]m$!+j kKD?Fh\\m7%7$$\"+R+*)\\\\F\\]m$!+7*)eq@Fh\\m7$$\"+h*4,0&F\\]m$!+GeI()> Fh\\m7$$\"+[5//\\F\\]m$!+%3!oC?Fh\\m7%7$$\"+k-))HfF\\]m$!+8C9q@Fh\\m7$ $\"+O(>,2'F\\]m$!+FBv()>Fh\\m7$$\"+)H#*f\"fF\\]m$!+T<,C?Fh\\m7%7$$\"+( \\=y!pF\\]m$!+&yt%p@Fh\\m7$$\"+.:=#4(F\\]m$!+b4U))>Fh\\m7$$\"+k%3%HpF \\]m$!+U[PB?Fh\\m7%7$$\"+P/U%)yF\\]m$!+]!e&o@Fh\\m7$$\"+j&zb6)F\\]m$!+ !pO$*)>Fh\\m7$$\"+]w\"R%zF\\]m$!+5l\"G-#Fh\\m7%7$$\"+d#3/'))F\\]m$!+B. Rn@Fh\\m7$$\"+VFh\\m7$$\"+Cq6f*)F\\]m$!+sFPA?Fh\\m 7%7$$\"+x_XO)*F\\]m$!+Mi)f;#Fh\\m7$$\"+sWN;5Fh\\m$!+1&3>*>Fh\\m7$$\"+0 Ogu**F\\]m$!+vd1A?Fh\\m7%7$$\"+\"*QJ\"3\"Fh\\m$!+\\(yV;#Fh\\m7$$\"+4ho =6Fh\\m$!+\"*f^$*>Fh\\m7$$\"+G0+*4\"Fh\\m$!+>M!>-#Fh\\m7%7$$\"+]54z6Fh \\m$!+MDhi@Fh\\m7$$\"+]*34A\"Fh\\m$!+1AG&*>Fh\\m7$$\"+^0]+7Fh\\m$!+j6) =-#Fh\\m7%7$$\"+:&3qF\"Fh\\m$!+*\\P2;#Fh\\m7$$\"+&[\"*HK\"Fh\\m$!+Ts:( *>Fh\\m7$$\"+\"zN>I\"Fh\\m$!+A_)>-#Fh\\m7%7$$\"+J\\3v8Fh\\m$!+\"*H!)e@ Fh\\m7$$\"+p]\"\\U\"Fh\\m$!+\\<4**>Fh\\m7$$\"+z*)G.9Fh\\m$!+-i>A?Fh\\m 7%7$$\"+A!GLZ\"Fh\\m$!+=N&o:#Fh\\m7$$\"+y>nE:Fh\\m$!+A7/,?Fh\\m7$$\"+& p\\X]\"Fh\\m$!+EC\\A?Fh\\m7%7$$\"+$3PFh\\m$!+FaO3?Fh\\m7$$\"+*QM'3>Fh\\m$!+\"zMT-#Fh\\m7%7$$\"+tX& o'>Fh\\m$!+:m!z9#Fh\\m7$$\"+Fa9L?Fh\\m$!+D\"))*4?Fh\\m7$$\"+\"GM%4?Fh \\m$!+8SeC?Fh\\m7%7$$\"+PdTu**Fe\\m$!+,4%o)>Fh\\m7$$\"+E%eD+\"F\\]m$!+ (yKE!=Fh\\m7$$\"+9B_k()Fe\\m$!+\">(RU=Fh\\m7%7$$\"+FG&)*)>F\\]m$!+QJ#o )>Fh\\m7$$\"+tr95?F\\]m$!+]0l-=Fh\\m7$$\"+i!z2)=F\\]m$!+\"yd?%=Fh\\m7% 7$$\"+]s\\xHF\\]m$!+!y[n)>Fh\\m7$$\"+]F]AIF\\]m$!+3\\s-=Fh\\m7$$\"+Ja) y)GF\\]m$!+M4`T=Fh\\m7%7$$\"+jG#3'RF\\]m$!+P*el)>Fh\\m7$$\"+Prc*>*oF\\]m$!+Lwm%)>Fh\\m7$$\"+\"Q/!3rF \\]m$!+bg![!=Fh\\m7$$\"+%=)=RpF\\]m$!+VLxQ=Fh\\m7%7$$\"+p;wlyF\\]m$!+s 0Y$)>Fh\\m7$$\"+J$QU8)F\\]m$!+;J,1=Fh\\m7$$\"+b1qbzF\\]m$!+*e\\#Q=Fh\\ m7%7$$\"+)HD%R))F\\]m$!+dJ'>)>Fh\\m7$$\"+-Zdg\"*F\\]m$!+J0^2=Fh\\m7$$ \"+\\_ms*)F\\]m$!+Xd)y$=Fh\\m7%7$$\"+uOx8)*F\\]m$!+W_@!)>Fh\\m7$$\"+LE i=5Fh\\m$!+W%e#4=Fh\\m7$$\"+m:e*)**F\\]m$!+kapP=Fh\\m7%7$$\"+8;%*y5Fh \\m$!+IZFy>Fh\\m7$$\"+(Qe57\"Fh\\m$!+e*)>6=Fh\\m7$$\"+`Dg+6Fh\\m$!+#)R nP=Fh\\m7%7$$\"+[lnw6Fh\\m$!+1u?w>Fh\\m7$$\"+_MKB7Fh\\m$!+#GmK\"=Fh\\m 7$$\"+#Qn@?\"Fh\\m$!+2I!y$=Fh\\m7%7$$\"+9]gu7Fh\\m$!+5y2u>Fh\\m7$$\"+' )\\RD8Fh\\m$!+yeR:=Fh\\m7$$\"+K4j.8Fh\\m$!+kk0Q=Fh\\m7%7$$\"+9Yts8Fh\\ m$!+'yU>(>Fh\\m7$$\"+'QlsU\"Fh\\m$!+-4`<=Fh\\m7$$\"+y6)\\S\"Fh\\m$!+Gc SQ=Fh\\m7%7$$\"+;<1r9Fh\\m$!+C\"[)p>Fh\\m7$$\"+%GQ*G:Fh\\m$!+kbi>=Fh\\ m7$$\"+mR@1:Fh\\m$!+hG#)Q=Fh\\m7%7$$\"+,`dp:Fh\\m$!+ex#y'>Fh\\m7$$\"+* pC/j\"Fh\\m$!+Ifk@=Fh\\m7$$\"+P4L2;Fh\\m$!+]QGR=Fh\\m7%7$$\"+m,Eo;Fh\\ m$!+mY!f'>Fh\\m7$$\"+M)RFh\\m7$$\"+02!H$=Fh\\m$!+k5QD=Fh\\m 7$$\"+7Fh\\m7$$\"+FX# R$>Fh\\m$!+wa2F=Fh\\m7$$\"+i@05>Fh\\m$!+q0vS=Fh\\m7%7$$\"+mAFh\\m$! +6F#3'>Fh\\m7$$\"+Mx#[.#Fh\\m$!+x4lG=Fh\\m7$$\"+'3y2,#Fh\\m$!+4zAT=Fh \\m7%7$$\"+]&G'o**Fe\\m$!+o(HE!=Fh\\m7$$\"+Xr8.5F\\]m$!+oGU=;Fh\\m7$$ \"+==\"yw)Fe\\m$!+e.;e;Fh\\m7%7$$\"+O>e()>F\\]m$!+qJg-=Fh\\m7$$\"+k!=C ,#F\\]m$!+m%\\%=;Fh\\m7$$\"+U%z?)=F\\]m$!+G![xl\"Fh\\m7%7$$\"+NbbsHF\\ ]m$!+HF\\-=Fh\\m7$$\"+lWWFIF\\]m$!+2*f&=;Fh\\m7$$\"+0\"\\2*GF\\]m$!+T' =rl\"Fh\\m7%7$$\"+N4Y_RF\\]m$!+FV@-=Fh\\m7$$\"+l!Rv/%F\\]m$!+4$Q)=;Fh \\m7$$\"+>._-RF\\]m$!+$3^jl\"Fh\\m7%7$$\"+vrCG\\F\\]m$!+X#y;!=Fh\\m7$$ \"+DGvr]F\\]m$!+\"Ru$>;Fh\\m7$$\"+`n(p\"\\F\\]m$!+F*Rbl\"Fh\\m7%7$$\"+ MZ3,fF\\]m$!+N7\"3!=Fh\\m7$$\"+m_\"*)4'F\\]m$!+,9C?;Fh\\m7$$\"+qTbLfF \\]m$!+31ya;Fh\\m7%7$$\"+LBEsoF\\]m$!+@^d*z\"Fh\\m7$$\"+nwtFrF\\]m$!+: vZ@;Fh\\m7$$\"+)ot:&pF\\]m$!+AT:a;Fh\\m7%7$$\"+Ur/VyF\\]m$!+Vg(zz\"Fh \\m7$$\"+eG&p:)F\\]m$!+$fwIi\"Fh\\m7$$\"+2&3.(zF\\]m$!+V`r`;Fh\\m7%7$$ \"+'GYX\"))F\\]m$!+)phgz\"Fh\\m7$$\"+9PX&=*F\\]m$!+Q4*\\i\"Fh\\m7$$\"+ qh1*)*)F\\]m$!+8#)[`;Fh\\m7%7$$\"+%>4wy*F\\]m$!+J)3Rz\"Fh\\m7$$\"+\"3R 7-\"Fh\\m$!+0Q9F;Fh\\m7$$\"+\"4E2+\"Fh\\m$!+P$oMl\"Fh\\m7%7$$\"+O\"zi2 \"Fh\\m$!+*e1;z\"Fh\\m7$$\"+k3sB6Fh\\m$!+ZgWH;Fh\\m7$$\"+ycW-6Fh\\m$!+ _2j`;Fh\\m7%7$$\"+hu.u6Fh\\m$!+&\\T#*y\"Fh\\m7$$\"+RD'fA\"Fh\\m$!+T6\" =j\"Fh\\m7$$\"+cw./7Fh\\m$!+!QRRl\"Fh\\m7%7$$\"+XA/s7Fh\\m$!+!R()oy\"F h\\m7$$\"+bx&zK\"Fh\\m$!+Y_;M;Fh\\m7$$\"+.%)[08Fh\\m$!+y_Na;Fh\\m7%7$$ \"+fYGq8Fh\\m$!+24g%y\"Fh\\m7$$\"+T`rH9Fh\\m$!+HFh\\m$!+WS'fk\"Fh\\m7$$\"+4nX6>Fh\\m$!+))z\\d;Fh\\ m7%7$$\"+\"fnN'>Fh\\m$!+D\"3Ox\"Fh\\m7$$\"+4CVO?Fh\\m$!+6XWZ;Fh\\m7$$ \"+6c47?Fh\\m$!+_;)zl\"Fh\\m7%7$$\"+QRjg**Fe\\m$!++#=%=;Fh\\m7$$\"+1m$ R+\"F\\]m$!+%Q8UV\"Fh\\m7$$\"+)zeBx)Fe\\m$!+1O\"RZ\"Fh\\m7%7$$\"+d*fW) >F\\]m$!+flP=;Fh\\m7$$\"+V+a:?F\\]m$!+D]DM9Fh\\m7$$\"+&RrQ)=F\\]m$!+ZG St9Fh\\m7%7$$\"+;5#e'HF\\]m$!+3c?=;Fh\\m7$$\"+%)*yT.$F\\]m$!+wfUM9Fh\\ m7$$\"+U9n%*GF\\]m$!+,9ks9Fh\\m7%7$$\"+?y@TRF\\]m$!+IBy<;Fh\\m7$$\"+!= #yeSF\\]m$!+a#\\[V\"Fh\\m7$$\"+\"f&>4RF\\]m$!+`$[hF\\]m$!+]')) oV\"Fh\\m7$$\"+./]YfF\\]m$!+Z%*4q9Fh\\m7%7$$\"+2!fv%oF\\]m$!+Of.9;Fh\\ m7$$\"+$*4W_rF\\]m$!+[cfQ9Fh\\m7$$\"+RLQnpF\\]m$!+w#f&p9Fh\\m7%7$$\"+& 42b\"yF\\]m$!+];#>h\"Fh\\m7$$\"+0H\\%=)F\\]m$!+M*42W\"Fh\\m7$$\"+bdU)) zF\\]m$!+u>Gp9Fh\\m7%7$$\"+\"\\!Q&y)F\\]m$!+JW]4;Fh\\m7$$\"+4&>Y@*F\\] m$!+`r7V9Fh\\m7$$\"+owy3!*F\\]m$!+(4l#p9Fh\\m7%7$$\"+>:&zv*F\\]m$!+?#4 pg\"Fh\\m7$$\"+[[?C5Fh\\m$!+kBsX9Fh\\m7$$\"+ihy-5Fh\\m$!+sLZp9Fh\\m7%7 $$\"+&*oNt5Fh\\m$!+faD/;Fh\\m7$$\"+0JkE6Fh\\m$!+DhP[9Fh\\m7$$\"+w(GX5 \"Fh\\m$!+S^&)p9Fh\\m7%7$$\"+&*eAr6Fh\\m$!+,3k,;Fh\\m7$$\"+0TxG7Fh\\m$ !+$y!*4X\"Fh\\m7$$\"+s=417Fh\\m$!+OiNq9Fh\\m7%7$$\"+%4%Qp7Fh\\m$!+q_8* f\"Fh\\m7$$\"+1fhI8Fh\\m$!+9j\\`9Fh\\m7$$\"+'=wuI\"Fh\\m$!+V'G4Z\"Fh\\ m7%7$$\"+;E!yO\"Fh\\m$!+AFy'f\"Fh\\m7$$\"+%Q(>K9Fh\\m$!+i)[eX\"Fh\\m7$ $\"+R@p39Fh\\m$!+&>M:Z\"Fh\\m7%7$$\"+c([kY\"Fh\\m$!+Veg%f\"Fh\\m7$$\"+ W7bL:Fh\\m$!+Td-e9Fh\\m7$$\"+%>b(4:Fh\\m$!+q\\9s9Fh\\m7%7$$\"+[-Hl:Fh \\m$!+f>h#f\"Fh\\m7$$\"+_(4Zj\"Fh\\m$!+D'>+Y\"Fh\\m7$$\"+_Eo5;Fh\\m$!+ `>us9Fh\\m7%7$$\"+.vHk;Fh\\m$!+1#)z!f\"Fh\\m7$$\"+(\\-dt\"Fh\\m$!+yL$= Y\"Fh\\m7$$\"+y;\\67=Fh\\m$!+\"p^QZ\"Fh\\m7%7$$ \"+z!4F'=Fh\\m$!+[;n(e\"Fh\\m7$$\"+@4HP>Fh\\m$!+O*f\\Y\"Fh\\m7$$\"+7m \"G\">Fh\\m$!+^VNu9Fh\\m7%7$$\"+>C2i>Fh\\m$!+uFL'e\"Fh\\m7$$\"+\"eFz.# Fh\\m$!+5))Hm9Fh\\m7$$\"+&HfL,#Fh\\m$!+x-#[Z\"Fh\\m7%7$$\"+m2:\\**Fe\\ m$!+md?M9Fh\\m7$$\"+B\\305F\\]m$!+mZ+]7Fh\\m7$$\"+4b*)y()Fe\\m$!+y7l*G \"Fh\\m7%7$$\"+wm+!)>F\\]m$!+lo8M9Fh\\m7$$\"+CL**>?F\\]m$!+nO2]7Fh\\m7 $$\"+MfV')=F\\]m$!+tP+*G\"Fh\\m7%7$$\"+/nLcHF\\]m$!+j'eQV\"Fh\\m7$$\"+ 'HjO/$F\\]m$!+p=N]7Fh\\m7$$\"+nSB+HF\\]m$!+Y92)G\"Fh\\m7%7$$\"+-UpDRF \\]m$!+fx=L9Fh\\m7$$\"+)z0V2%F\\]m$!+tF-^7Fh\\m7$$\"+)[=&=RF\\]m$!+s1/ (G\"Fh\\m7%7$$\"+H7Z!*[F\\]m$!+rM(>V\"Fh\\m7$$\"+r(G&4^F\\]m$!+hqB_7Fh \\m7$$\"+Hu8S\\F\\]m$!+Zq5'G\"Fh\\m7%7$$\"+)3HL&eF\\]m$!++'e,V\"Fh\\m7 $$\"+74nYhF\\]m$!+K>0a7Fh\\m7$$\"+\"ffO'fF\\]m$!+ibU&G\"Fh\\m7%7$$\"+[ Vt;oF\\]m$!+I0!yU\"Fh\\m7$$\"+_cE$=(F\\]m$!+-+Tc7Fh\\m7$$\"+#e3w)pF\\] m$!+us2&G\"Fh\\m7%7$$\"+jMc#y(F\\]m$!+'HX]U\"Fh\\m7$$\"+PlV<#)F\\]m$!+ O_;f7Fh\\m7$$\"+&GA2,)F\\]m$!+)zl]G\"Fh\\m7%7$$\"+&*\\$>v)F\\]m$!+*\\v ?U\"Fh\\m7$$\"+0]1[#*F\\]m$!+L]8i7Fh\\m7$$\"+w'=@.*F\\]m$!+8\"R`G\"Fh \\m7%7$$\"+:rFD(*F\\]m$!+>>1>9Fh\\m7$$\"+*Gsu-\"Fh\\m$!+8'[^E\"Fh\\m7$ $\"+AB805Fh\\m$!+5,#eG\"Fh\\m7%7$$\"+hCDq5Fh\\m$!+*)f8;9Fh\\m7$$\"+Rvu H6Fh\\m$!+VX2o7Fh\\m7$$\"+]%>o5\"Fh\\m$!+i7V'G\"Fh\\m7%7$$\"+(3L$o6Fh \\m$!+MKQ89Fh\\m7$$\"+8pmJ7Fh\\m$!+)HF3F\"Fh\\m7$$\"+*H\"G37Fh\\m$!+; \"3rG\"Fh\\m7%7$$\"+nJsm7Fh\\m$!+D%\\3T\"Fh\\m7$$\"+LoFL8Fh\\m$!+26Ot7 Fh\\m7$$\"+xz`48Fh\\m$!+WL!yG\"Fh\\m7%7$$\"+eZPl8Fh\\m$!+@7b39Fh\\m7$$ \"+U_iM9Fh\\m$!+6$fcF\"Fh\\m7$$\"+2Wh59Fh\\m$!+=a[)G\"Fh\\m7%7$$\"+%pV UY\"Fh\\m$!+Ek[19Fh\\m7$$\"+1jvN:Fh\\m$!+1Tsx7Fh\\m7$$\"+Gf`6:Fh\\m$!+ Y_8*G\"Fh\\m7%7$$\"+'p\"Hj:Fh\\m$!+q>k/9Fh\\m7$$\"+/$3nj\"Fh\\m$!+i&o& z7Fh\\m7$$\"+=gK7;Fh\\m$!+4Eu*G\"Fh\\m7%7$$\"+9n[i;Fh\\m$!+4%**HS\"Fh \\m7$$\"+'G8vt\"Fh\\m$!+B6@\"G\"Fh\\m7$$\"+_`+8Q=Fh\\m$!+R@n#G\"Fh\\m7$$\"+ 4;f8=Fh\\m$!+bk\"3H\"Fh\\m7%7$$\"+\"\\<7'=Fh\\m$!+1(Q-S\"Fh\\m7$$\"+4D yQ>Fh\\m$!+E=(RG\"Fh\\m7$$\"+_'*49>Fh\\m$!+yRG\"H\"Fh\\m7%7$$\"+&f92'> Fh\\m$!+Y83*R\"Fh\\m7$$\"+0aGR?Fh\\m$!+'=H^G\"Fh\\m7$$\"+e=a9?Fh\\m$!+ *e3F\\]m$!+E\"p)\\7Fh \\m7$$\"+O`kE?F\\]m$!+b.#f1\"Fh\\m7$$\"+(=&G!*=F\\]m$!+W$>X5\"Fh\\m7%7 $$\"+dfWUHF\\]m$!+xxQ\\7Fh\\m7$$\"+VSbdIF\\]m$!+.$RF\\]m$!+FO@-6Fh\\m7%7$$\"+Kd&4'[F\\]m$!+_pOY7F h\\m7$$\"+oU/R^F\\]m$!+GDUp5Fh\\m7$$\"+.pwe\\F\\]m$!+l(G85\"Fh\\m7%7$$ \"+.mN=eF\\]m$!+HrqV7Fh\\m7$$\"+(RV;='F\\]m$!+^B3s5Fh\\m7$$\"+H)Hl)fF \\]m$!+\\](35\"Fh\\m7%7$$\"+q5*)ynF\\]m$!+dY]S7Fh\\m7$$\"+J*36A(F\\]m$ !+B[Gv5Fh\\m7$$\"+(\\_K,(F\\]m$!+=L(35\"Fh\\m7%7$$\"+AlEWxF\\]m$!+k5/P 7Fh\\m7$$\"+yMtb#)F\\]m$!+;%[(y5Fh\\m7$$\"+lZeP!)F\\]m$!+!eU75\"Fh\\m7 %7$$\"+R!*)\\r)F\\]m$!+S6dL7Fh\\m7$$\"+h4,&G*F\\]m$!+S$=A3\"Fh\\m7$$\" +4R*)e!*F\\]m$!+y;'=5\"Fh\\m7%7$$\"+#G\"y!p*F\\]m$!+\">u-B\"Fh\\m7$$\" +s=#4.\"Fh\\m$!+*G:b3\"Fh\\m7$$\"+$Q4x+\"Fh\\m$!+vhh-6Fh\\m7%7$$\"+&H* 4n5Fh\\m$!+?0DF7Fh\\m7$$\"+02!H8\"Fh\\m$!+g*Q&)3\"Fh\\m7$$\"+7M5\"Fh\\m7%7$$\"+Nx[l6Fh\\m$!+Z)RXA\"Fh\\m7$$\"+lA^M7Fh\\m$!+L' \\74\"Fh\\m7$$\"+BL_57Fh\\m$!+/S@/6Fh\\m7%7$$\"+$\\tTE\"Fh\\m$!+JL9A7F h\\m7$$\"+2l#eL\"Fh\\m$!+\\hk$4\"Fh\\m7$$\"+BPf68Fh\\m$!+cv'\\5\"Fh\\m 7%7$$\"+oo4j8Fh\\m$!+E6/?7Fh\\m7$$\"+KJ!pV\"Fh\\m$!+a$[d4\"Fh\\m7$$\"+ b%*[79Fh\\m$!+lOm06Fh\\m7%7$$\"+'H4AY\"Fh\\m$!+/S?=7Fh\\m7$$\"+/2zP:Fh \\m$!+wae(4\"Fh\\m7$$\"+@?C8:Fh\\m$!+SlH16Fh\\m7%7$$\"+^AZh:Fh\\m$!+(> +m@\"Fh\\m7$$\"+\\x_Q;Fh\\m$!+$G*=*4\"Fh\\m7$$\"+vv(Qh\"Fh\\m$!+\\k'o5 \"Fh\\m7%7$$\"+?b&3m\"Fh\\m$!+6!*>:7Fh\\m7$$\"+![W\"RFh\\m$!+VM*G5\"Fh\\m7$$\"+c_F: >Fh\\m$!+L(R#36Fh\\m7%7$$\"+ie^f>Fh\\m$!+a$[>@\"Fh\\m7$$\"+QT[S?Fh\\m$ !+E6%Q5\"Fh\\m7$$\"+W\"=c,#Fh\\m$!+;Ig36Fh\\m7%7$$\"+,1)Q!**Fe\\m$!+cC xl5Fh\\m7$$\"+S>h45F\\]m$!+7(ff\"))F\\]m7$$\"+u%HZ!))Fe\\m$!+[pG5#*F\\ ]m7%7$$\"+uf\"G'>F\\]m$!+DW`l5Fh\\m7$$\"+ES=P?F\\]m$!+F+M=))F\\]m7$$\" +7!Hk*=F\\]m$!+&))Q*)>*F\\]m7%7$$\"+7S9@HF\\]m$!+%zOY1\"Fh\\m7$$\"+))f &)yIF\\]m$!+OjJF))F\\]m7$$\"+*pu7#HF\\]m$!+.t$[=*F\\]m7%7$$\"+ZCZrQF\\ ]m$!+SWpi5Fh\\m7$$\"+`v_GTF\\]m$!+r)Rn%))F\\]m7$$\"+(*Q2_RF\\]m$!+Q^(H <*F\\]m7%7$$\"+_3g?[F\\]m$!+fmlf5Fh\\m7$$\"+[\"*Rz^F\\]m$!+'o2Rx&F\\]m$!+&4Ne0\"Fh\\m 7$$\"+4G4EiF\\]m$!+@LL:*)F\\]m7$$\"+p7q;gF\\]m$!+&QNp;*F\\]m7%7$$\"++r =MnF\\]m$!+pap^5Fh\\m7$$\"++H\"eE(F\\]m$!+%eHn&*)F\\]m7$$\"+?,%[/(F\\] m$!+$R9@<*F\\]m7%7$$\"+95'>q(F\\]m$!+vzjZ5Fh\\m7$$\"+')*Q!)H)F\\]m$!+@ XI(**)F\\]m7$$\"++&='o!)F\\]m$!+1*y-=*F\\]m7%7$$\"+$oekn)F\\]m$!+(42R/ \"Fh\\m7$$\"+<8aB$*F\\]m$!+0LhM!*F\\]m7$$\"+L89)3*F\\]m$!+=!)o*=*F\\]m 7%7$$\"+aXYc'*F\\]m$!+7qgS5Fh\\m7$$\"+XNNM5Fh\\m$!+]Thn!*F\\]m7$$\"+Wc R55Fh\\m$!+b7>*>*F\\]m7%7$$\"+p!yS1\"Fh\\m$!+Z#f8\"Fh \\m$!++o;'4*F\\]m7$$\"+*Rs;6\"Fh\\m$!+:u:3#*F\\]m7%7$$\"+<,%G;\"Fh\\m$ !+f#4`.\"Fh\\m7$$\"+$))frB\"Fh\\m$!+#o\"f?\"*F\\]m7$$\"+$y0F@\"Fh\\m$! +;\\I;#*F\\]m7%7$$\"+gR&=E\"Fh\\m$!+E&HK.\"Fh\\m7$$\"+Sg9Q8Fh\\m$!+8!* QT\"*F\\]m7$$\"+rra88Fh\\m$!+F_bB#*F\\]m7%7$$\"+*4g5O\"Fh\\m$!+A&f9.\" Fh\\m7$$\"+,*R*Q9Fh\\m$!+^!*3f\"*F\\]m7$$\"+&\\PUT\"Fh\\m$!+&)\\$*H#*F \\]m7%7$$\"+'39/Y\"Fh\\m$!+l+&*H5Fh\\m7$$\"+9feR:Fh\\m$!+EO=u\"*F\\]m7 $$\"+J'3[^\"Fh\\m$!+e$=bB*F\\]m7%7$$\"+$y#))f:Fh\\m$!+$He'G5Fh\\m7$$\" +*F\\]m7$$\"+Iho:Fh\\m$!+W96;#*F\\]m7$$\"+gmJ;>Fh\\m$!+_Rm^#*F\\]m7%7$$\" +\\2\\e>Fh\\m$!+!zJ]-\"Fh\\m7$$\"+^#4:/#Fh\\m$!+yjOB#*F\\]m7$$\"+=mc;? Fh\\m$!+!)oaa#*F\\]m7%7$$\"+!HF\\]m$!+oz :5))F\\]m7$$\"+^m?b?F\\]m$!+!y:$zpF\\]m7$$\"+]d12>F\\]m$!+E1G]tF\\]m7% 7$$\"+*e*z')GF\\]m$!+eO(=z)F\\]m7$$\"+6/?8JF\\]m$!+!4+w*pF\\]m7$$\"+<* GC%HF\\]m$!+X*RRL(F\\]m7%7$$\"+&z3R#QF\\]m$!+O*ynv)F\\]m7$$\"+074wTF\\ ]m$!+7[pKqF\\]m7$$\"+a+&G)RF\\]m$!+S`([K(F\\]m7%7$$\"+#[lnw%F\\]m$!+$ \\U%4()F\\]m7$$\"+=XBL_F\\]m$!+b7.!3(F\\]m7$$\"+=Qn@]F\\]m$!+.&)RDtF\\ ]m7%7$$\"+ZCU?dF\\]m$!+#fZ$e')F\\]m7$$\"+avdziF\\]m$!+ch7JrF\\]m7$$\"+ RS)[0'F\\]m$!+vk-LtF\\]m7%7$$\"+hH5&o'F\\]m$!+'ov,h)F\\]m7$$\"+Rq*[J(F \\]m$!+i!)HzrF\\]m7$$\"+atW\"3(F\\]m$!+#ytSM(F\\]m7%7$$\"+po&)ewF\\]m$ !+]Z5o&)F\\]m7$$\"+JJ9T$)F\\]m$!+)**o8A(F\\]m7$$\"+#=Q?5)F\\]m$!+_/%eN (F\\]m7%7$$\"+%p3%R')F\\]m$!+$[\"zK&)F\\]m7$$\"+18fg$*F\\]m$!+lAocsF\\ ]m7$$\"+lv&y6*F\\]m$!+Ii!pO(F\\]m7%7$$\"+Tr'[i*F\\]m$!+/$yO])F\\]m7$$ \"+'G8v.\"Fh\\m$!+Waz&G(F\\]m7$$\"+_`+85Fh\\m$!+kirwtF\\]m7%7$$\"+WOQh 5Fh\\m$!+\\D\")z%)F\\]m7$$\"+cjhQ6Fh\\m$!+*>h'4tF\\]m7$$\"+rY&R6\"Fh\\ m$!+W)R(F\\]m7%7$$\" +ejLf8Fh\\m$!+F8oI%)F\\]m7$$\"+UOmS9Fh\\m$!+@CzetF\\]m7$$\"+PAy:9Fh\\m $!+1kf.uF\\]m7%7$$\"+&>3*e9Fh\\m$!+XE[>%)F\\]m7$$\"+0=4T:Fh\\m$!+.6**p tF\\]m7$$\"+#)p<;:Fh\\m$!+5T(zS(F\\]m7%7$$\"+=!e&e:Fh\\m$!+VJ05%)F\\]m 7$$\"+#)>WT;Fh\\m$!+11UztF\\]m7$$\"+*\\.lh\"Fh\\m$!+iyq6uF\\]m7%7$$\"+ A#o#e;Fh\\m$!+R]0-%)F\\]m7$$\"+y%=Fh\\m$!+c1 D%R(F\\]m7$$\"+9l+<=Fh\\m$!+-amFh\\m$!+nc7+uF\\]m7$$\"+CB?<>Fh\\m$!+PO0?uF\\]m7%7$$\" +lmkd>Fh\\m$!+)*RE%Q)F\\]m7$$\"+NLNU?Fh\\m$!+](4_S(F\\]m7$$\"+?-PbF\\]m7%7$$\"++vy5>F\\]m$!+&e/*epF\\ ]m7$$\"++D@*3#F\\]m$!+P'ej9&F\\]m7$$\"+l\")eF>F\\]m$!+U;q(\\&F\\]m7%7$ $\"+&>o#HGF\\]m$!+rVK=pF\\]m7$$\"+0=tqJF\\]m$!+_)Qp=&F\\]m7$$\"+!*eJzH F\\]m$!+C$oJ[&F\\]m7%7$$\"+0\"3dv$F\\]m$!+rcEcoF\\]m7$$\"+&*=HWUF\\]m$ !+^v**[_F\\]m7$$\"+zdWHSF\\]m$!+g%yW[&F\\]m7%7$$\"+e0s+ZF\\]m$!+ftY!z' F\\]m7$$\"+U%z#*H&F\\]m$!+jez9`F\\]m7$$\"+\"z_&p]F\\]m$!+b?Y'\\&F\\]m7 %7$$\"+JB(Gm&F\\]m$!+9u#Gt'F\\]m7$$\"+pw7PjF\\]m$!+3eVs`F\\]m7$$\"+>[$ ))4'F\\]m$!+nIr6bF\\]m7%7$$\"+%Hosj'F\\]m$!+rfb'o'F\\]m7$$\"+1rF\\]m$!+bq:EbF\\]m7%7$$\"+/eq>wF\\]m$!+e1h]mF \\]m7$$\"+'>%H!Q)F\\]m$!+kDlaaF\\]m7$$\"+!onW8)F\\]m$!+-'\\%QbF\\]m7%7 $$\"+Q&\\tg)F\\]m$!+A%oGi'F\\]m7$$\"+i/l#R*F\\]m$!++[R#[&F\\]m7$$\"+V& Q_9*F\\]m$!+6()[[bF\\]m7%7$$\"+s8T)f*F\\]m$!+?'R8g'F\\]m7$$\"+j)e,/\"F h\\m$!+-O#R]&F\\]m7$$\"+9GK:5Fh\\m$!+3!zlb&F\\]m7%7$$\"+TsxX\"Fh\\m$!+$>\"GWlF\\]m7$$\"+B3GU:Fh\\m$!+H?)4c&F\\ ]m7$$\"+-.I<:Fh\\m$!+F#e\"zbF\\]m7%7$$\"+t^^d:Fh\\m$!+3pFQlF\\]m7$$\"+ F[[U;Fh\\m$!+9j)pc&F\\]m7$$\"+du\\<;Fh\\m$!+*3B;e&F\\]m7%7$$\"+RlMd;Fh \\m$!+,[BLlF\\]m7$$\"+hMlUFh\\m$!+h\"[*zbF\\]m7$$\"+2k\"z\">Fh\\m$!+W#)*pe&F\\]m7%7$$\"+&4& )p&>Fh\\m$!+QiF\\]m$!+d`,UOF\\]m7%7$$\"+MoW OFF\\]m$!+liB$*\\F\\]m7$$\"+mJbjKF\\]m$!+Jk\"yU$F\\]m7$$\"+!Q1K/$F\\]m $!+*fm`k$F\\]m7%7$$\"+_H*4n$F\\]m$!+ZT3/\\F\\]m7$$\"+[q+HVF\\]m$!+\\&o p^$F\\]m7$$\"+;rT#4%F\\]m$!+#[rdm$F\\]m7%7$$\"+oeYLYF\\]m$!+m\\)p$[F\\ ]m7$$\"+KT`m`F\\]m$!+Ix1%e$F\\]m7$$\"+83!G7&F\\]m$!+bO`'o$F\\]m7%7$$\" +vX]6cF\\]m$!+I*R.z%F\\]m7$$\"+Da\\)Q'F\\]m$!+mFrIOF\\]m7$$\"+&)HeThF \\]m$!+Xq'Gq$F\\]m7%7$$\"+(3Qzf'F\\]m$!+')p0eZF\\]m7$$\"+8>1-uF\\]m$!+ 5d*Hm$F\\]m7$$\"+pil`rF\\]m$!+SL#\\r$F\\]m7%7$$\"+Z>3*e(F\\]m$!+>@FNZF \\]m7$$\"+`!=4T)F\\]m$!+x0y&o$F\\]m7$$\"+>)p<;)F\\]m$!+%ejPs$F\\]m7%7$ $\"+Ui,$e)F\\]m$!+hcx=ZF\\]m7$$\"+eP)pT*F\\]m$!+NqF-PF\\]m7$$\"+-yWn\" *F\\]m$!+\\MKIPF\\]m7%7$$\"+(z\"py&*F\\]m$!+6j_1ZF\\]m7$$\"+?38U5Fh\\m $!+&QEXr$F\\]m7$$\"+7i:<5Fh\\m$!+brFNPF\\]m7%7$$\"+d/bd5Fh\\m$!+!\\)p<7Fh\\m$!+a(p?u$F\\]m7%7$$\"+^;7d7Fh\\m$!+A.H%o%F\\]m7$$\"+\\$yGM\" Fh\\m$!+uBwOPF\\]m7$$\"+D=)yJ\"Fh\\m$!+7@WWPF\\]m7%7$$\"+\"[tpN\"Fh\\m $!+`(4(zYF\\]m7$$\"+>l-V9Fh\\m$!+VHMTPF\\]m7$$\"+,!G!=9Fh\\m$!+uoNYPF \\]m7%7$$\"+gU&oX\"Fh\\m$!+v(zfn%F\\]m7$$\"+Sd9V:Fh\\m$!+@H2XPF\\]m7$$ \"+>i9=:Fh\\m$!+\"oAzu$F\\]m7%7$$\"+5pvc:Fh\\m$!+\"*R!Hn%F\\]m7$$\"+!4 VKk\"Fh\\m$!+0([\"[PF\\]m7$$\"+dJC=;Fh\\m$!+(G=#\\PF\\]m7%7$$\"+)Qwml \"Fh\\m$!+!3R.n%F\\]m7$$\"+7OKVFh\\m$!+M.raPF\\]m7$$\"+J$[%=>Fh\\m$!+ga*>v$F\\]m7%7$$\"+nN]c>Fh \\m$!+r)oZm%F\\]m7$$\"+Lk\\V?Fh\\m$!+DQGcPF\\]m7$$\"+0s\\=?Fh\\m$!+*3k Ev$F\\]m7%7$$\"+=nhd')Fe\\m$!+m$ecD$F\\]m7$$\"+G$QU8\"F\\]m$!+/Q=\"[\" F\\]m7$$\"+Il+d&*Fe\\m$!+L&[N!=F\\]m7%7$$\"+;Iv&p\"F\\]m$!+H-L*4$F\\]m 7$$\"+%)pC/BF\\]m$!+T>^P;F\\]m7$$\"+j$4L2#F\\]m$!+U6*Q\"=F\\]m7%7$$\"+ Ur'[i#F\\]m$!+Q #=F\\]m7$$\"+#eXGF\\]m7$$\"+m%*zFuF\\]m$!+ C![;*=F\\]m7$$\"+[>&y<(F\\]m$!+/R3,>F\\]m7%7$$\"+XxWpvF\\]m$!+C+rOGF\\ ]m7$$\"+bAbI%)F\\]m$!+Y@8+>F\\]m7$$\"+hTc!=)F\\]m$!+hli/>F\\]m7%7$$\"+ '4pvc)F\\]m$!+G()zIGF\\]m7$$\"+/4VK%*F\\]m$!+UM/1>F\\]m7$$\"+y:V#=*F\\ ]m$!+CI62>F\\]m7%7$$\"+&4Iic*F\\]m$!+fH_EGF\\]m7$$\"+\"*pPV5Fh\\m$!+6# >.\">F\\]m7$$\"+1rP=5Fh\\m$!+&o?*3>F\\]m7%7$$\"+9U_c5Fh\\m$!+;QLBGF\\] m7$$\"+'yvM9\"Fh\\m$!+a$3N\">F\\]m7$$\"+.kZ=6Fh\\m$!+2RF5>F\\]m7%7$$\" +N#\\k:\"Fh\\m$!+DO*3#GF\\]m7$$\"+l2bV7Fh\\m$!+X&[f\">F\\]m7$$\"+K?b=7 Fh\\m$!+q@J6>F\\]m7%7$$\"+')4Rc7Fh\\m$!+\\e)*=GF\\]m7$$\"+9!4OM\"Fh\\m $!+@j&y\">F\\]m7$$\"+]4h=8Fh\\m$!+.c77>F\\]m7%7$$\"+L[Mc8Fh\\m$!+TmY>F\\]m7$$\"+Nxl=9Fh\\m$!+DWx7>F\\]m7%7$$\" +TwIc9Fh\\m$!+2vB;GF\\]m7$$\"+fBpV:Fh\\m$!+jYg?>F\\]m7$$\"+/bp=:Fh\\m$ !+^+I8>F\\]m7%7$$\"+JsFc:Fh\\m$!+8#H_\"GF\\]m7$$\"+pFsV;Fh\\m$!+dHh@>F \\]m7$$\"+Iks=;Fh\\m$!+'pJP\">F\\]m7%7$$\"+[?Dc;Fh\\m$!+p>R9GF\\]m7$$ \"+_zuVF\\]m7$$\"+r?v=F\\]m7%7$$\"+f4BcF\\]m7$$\"+lNx==Fh\\m$!+[F\\]m7%7$$\"+@J@c=Fh\\m$!+>P48GF\\]m7$$\"+zoyV>Fh\\m$!+^%[P#>F\\]m7$$ \"+hFh\\m$!+^sk9>F\\]m7%7$$\"+**y>c>Fh\\m$!+,Ze7GF\\]m7$$\"+,@!Q/# Fh\\m$!+puDC>F\\]m7$$\"++t!)=?Fh\\m$!+bd'[\">F\\]m7%7$$\"+'\\>3*eFe\\m $!+-;1^5F\\]m7$$\"+]!=4T\"F\\]m$!)D/q:Fe\\m7$$\"+;)p<;\"F\\]m$!+\\aIbR !#77%7$$\"+(4pvc\"F\\]m$!+xY$p))*Fe\\m7$$\"+/4VKCF\\]m$!*jP(R(Fd]al7%7$$\"+&\\15c(F\\]m$!+DS4s'*Fe\\m7$$\"+0N**Q%)F\\]m$!*:CA a)Fe\\m7$$\"+%=o!*=)F\\]m$!+_+n;uFd]al7%7$$\"+Eb\"4c)F\\]m$!+?!>!p'*Fe \\m7$$\"+uW3R%*F\\]m$!*?uHd)Fe\\m7$$\"+%\\h\"*=*F\\]m$!+fb\"*HuFd]al7% 7$$\"+s/&3c*F\\]m$!+6$=om*Fe\\m7$$\"+`\\\"R/\"Fh\\m$!*H\")\\f)Fe\\m7$$ \"+DG#*=5Fh\\m$!+\"Q(RRuFd]al7%7$$\"+N-3c5Fh\\m$!+5%*=l'*Fe\\m7$$\"+l( >R9\"Fh\\m$!*Iq7h)Fe\\m7$$\"+kx#*=6Fh\\m$!+&z;kW(Fd]al7%7$$\"+vl2c6Fh \\m$!+P,&Rm*Fe\\m7$$\"+DM#RC\"Fh\\m$!*.jOi)Fe\\m7$$\"+@:$*=7Fh\\m$!+(* yv^uFd]al7%7$$\"+FP2c7Fh\\m$!+ya)Hm*Fe\\m7$$\"+ti#RM\"Fh\\m$!*i4Lj)Fe \\m7$$\"+XW$*=8Fh\\m$!+ye\"fX(Fd]al7%7$$\"+o92c8Fh\\m$!+9*>Am*Fe\\m7$$ \"+K&GRW\"Fh\\m$!*El4k)Fe\\m7$$\"+kn$*=9Fh\\m$!+yf@fuFd]al7%7$$\"+X'pg X\"Fh\\m$!+6Agh'*Fe\\m7$$\"+b.$Ra\"Fh\\m$!*HUrk)Fe\\m7$$\"+O'Q*=:Fh\\m $!+Z)y=Y(Fd]al7%7$$\"+`\"ogb\"Fh\\m$!+4m4h'*Fe\\m7$$\"+Z=$Rk\"Fh\\m$!* J)>_')Fe\\m7$$\"+p,%*=;Fh\\m$!+)eeSY(Fd]al7%7$$\"+T$R%=Fh\\m$!*5,*f')Fe\\m7$$\"+- D%*==Fh\\m$!+x&ztY(Fd]al7%7$$\"+/]1c=Fh\\m$!+z!H+m*Fe\\m7$$\"+'*\\$R%> Fh\\m$!*htGm)Fe\\m7$$\"+.M%*=>Fh\\m$!+?7mouFd]al7%7$$\"+cU1c>Fh\\m$!+ \"Gv(f'*Fe\\m7$$\"+Wd$R/#Fh\\m$!*f6am)Fe\\m7$$\"+rT%*=?Fh\\m$!+?bvpuFd ]al7%7$$\"+&RCU?(Fe\\m$\"+>ty@bFe\\m7$$\"+hvdz7F\\]m$\"+],Sz?F\\]m7$$ \"+WS)[0\"F\\]m$\"+Q)*\\x=F\\]m7%7$$\"+y=L0;F\\]m$\"+q!*)H](Fe\\m7$$\" +A\"oYR#F\\]m$\"+v*z7)=F\\]m7$$\"+om-Z@F\\]m$\"+Z/<==F\\]m7%7$$\"+.#e- e#F\\]m$\"+kA.`\")Fe\\m7$$\"+)zT(>MF\\]m$\"+ccF;=F\\]m7$$\"+R^1qJF\\]m $\"+74'Gz\"F\\]m7%7$$\"+PebrNF\\]m$\"+=*[)4%)Fe\\m7$$\"+jTWGWF\\]m$\"+ !*Rf!z\"F\\]m7$$\"+QY[yTF\\]m$\"+,uI#y\"F\\]m7%7$$\"+&4pvc%F\\]m$\"+#* z6M&)Fe\\m7$$\"+04VKaF\\]m$\"+$3n\"yt=*F\\]m$\"+9=SqAQC\"Fh\\m$\"+p+Gfd0paQW\"Fh\\m$ \"+]^?eFh\\m $\"+K7%ov\"F\\]m7$$\"+;?!*=>Fh\\m$\"+'p1!oFh\\m$\"+ 0'e*[()Fe\\m7$$\"+]$**Q/#Fh\\m$\"+AIoc.gsRF\\]m7$$\"+?Qn@?F\\]m$\"+uIBFPF\\]m7%7$$\"+\\H* 4n#F\\]m$\"+6pLkCF\\]m7$$\"+_q+HLF\\]m$\"+)\\_9&QF\\]m7$$\"+>rT#4$F\\] m$\"+p&\\Eq$F\\]m7%7$$\"+Rr'[i$F\\]m$\"+yK&*[DF\\]m7$$\"+hG8vVF\\]m$\" +Ih$ow$F\\]m7$$\"+)R&F\\]m$\"+B&G\\r$F\\]m7$$\"+&)[<]^F\\]m$\"+]d5dOF \\]m7%7$$\"+Y>3*e&F\\]m$\"+O*[Jj#F\\]m7$$\"+a!=4T'F\\]m$\"+s/k#o$F\\]m 7$$\"+?)p<;'F\\]m$\"+nulWOF\\]m7%7$$\"+%o<9e'F\\]m$\"+hS7aEF\\]m7$$\"+ ;Be=uF\\]m$\"+Z`mhOF\\]m7$$\"+$)>'*orF\\]m$\"+KWHOOF\\]m7%7$$\"+ZmYwvF \\]m$\"+#en$oEF\\]m7$$\"+`L`B%)F\\]m$\"+E=UZOF\\]m7$$\"+3Aqt\")F\\]m$ \"+>')\\IOF\\]m7%7$$\"+R&*3t&)F\\]m$\"+Z_UyEF\\]m7$$\"+h/\"pU*F\\]m$\" +iTOPOF\\]m7$$\"+a>)p<*F\\]m$\"+)H^ji$F\\]m7%7$$\"+`\\oq&*F\\]m$\"+xqw &o#F\\]m7$$\"+0:$H/\"Fh\\m$\"+JB-IOF\\]m7$$\"+sT$z,\"Fh\\m$\"+[fHBOF\\ ]m7%7$$\"+r7*o0\"Fh\\m$\"+`!z7p#F\\]m7$$\"+H(3J9\"Fh\\m$\"+b.^COF\\]m7 $$\"+h%4\"=6Fh\\m$\"+%*o)4i$F\\]m7%7$$\"+5pvc6Fh\\m$\"+iq^&p#F\\]m7$$ \"+!4VKC\"Fh\\m$\"+YBF?OF\\]m7$$\"+dJC=7Fh\\m$\"+lF?>OF\\]m7%7$$\"+AEl c7Fh\\m$\"+VE%))p#F\\]m7$$\"+ytMV8Fh\\m$\"+ln%ph$F\\]m7$$\"+@uM=8Fh\\m $\"+tuzFh\\m$\"+%*)3mg$F\\]m7$$ \"+Dzm=>Fh\\m$\"+?(*R8OF\\]m7%7$$\"+TwIc>Fh\\m$\"+$Gy+r#F\\]m7$$\"+fBp V?Fh\\m$\"+D6r0OF\\]m7$$\"+/bp=?Fh\\m$\"+Qd,8OF\\]m7%7$$\"+wZjY'*Fe\\m $\"+'R]73%F\\]m7$$\"+AlLN5F\\]m$\"+Q&\\(=fF\\]m7$$\"+s\"zM&*)Fe\\m$\"+ -F>PbF\\]m7%7$$\"+>1(o(=F\\]m$\"+k>J2TF\\]m7$$\"+\"QHJ7#F\\]m$\"+rzo#* eF\\]m7$$\"+!Gi'[>F\\]m$\"+Zq%Gc&F\\]m7%7$$\"+=n&3y#F\\]m$\"+``7sTF\\] m7$$\"+#GV\">KF\\]m$\"+\"euy#eF\\]m7$$\"+Yq*=,$F\\]m$\"+1cJqbF\\]m7%7$ $\"+f(\\\"3PF\\]m$\"+JP8_UF\\]m7$$\"+T-&=H%F\\]m$\"+.i'yu&F\\]m7$$\"+[ #zR1%F\\]m$\"+S`VebF\\]m7%7$$\"+A@EhYF\\]m$\"+:U_AVF\\]m7$$\"+zytQ`F\\ ]m$\"+?dZxcF\\]m7$$\"+Pp6+^F\\]m$\"+@y6SbF\\]m7%7$$\"+!R0?j&F\\]m$\"+[ NXwVF\\]m7$$\"+5Y*zO'F\\]m$\"+'QYNi&F\\]m7$$\"+8T-ChF\\]m$\"+oS,BbF\\] m7%7$$\"+UHL8mF\\]m$\"+,Q0;WF\\]m7$$\"+eqm'Q(F\\]m$\"+Lh%Re&F\\]m7$$\" +ua)*RrF\\]m$\"+\"Qg\"4bF\\]m7%7$$\"+,E%4g(F\\]m$\"+u21XWF\\]m7$$\"+*R d!*R)F\\]m$\"+g\"R\\b&F\\]m7$$\"++t%4:)F\\]m$\"+u)>%)\\&F\\]m7%7$$\"+s lQ#f)F\\]m$\"+G*zlY%F\\]m7$$\"+GMh2%*F\\]m$\"+1+ULbF\\]m7$$\"+<*=(e\"* F\\]m$\"+k!f,\\&F\\]m7%7$$\"+8@E'e*F\\]m$\"+4w#G[%F\\]m7$$\"+*yt8/\"Fh \\m$\"+DB<<7Fh\\m$\"+C2![Z&F\\]m7%7$$\"+d]cd7Fh\\m$\"+ep(G^%F \\]m7$$\"+V\\VU8Fh\\m$\"+wH7([&F\\]m7$$\"+>\"\\uJ\"Fh\\m$\"+/mhraF\\]m 7%7$$\"+nYNd8Fh\\m$\"+x?:>XF\\]m7$$\"+L`kU9Fh\\m$\"+dy%3[&F\\]m7$$\"+p Nl<9Fh\\m$\"+&fF!paF\\]m7%7$$\"+Na=d9Fh\\m$\"+uDGCXF\\]m7$$\"+lX\"Ga\" Fh\\m$\"+gtrvaF\\]m7$$\"+]\">y^\"Fh\\m$\"+F!)*oY&F\\]m7%7$$\"++t/d:Fh \\m$\"+qp_GXF\\]m7$$\"++F&Hk\"Fh\\m$\"+kHZraF\\]m7$$\"+t]&zh\"Fh\\m$\" +bw7laF\\]m7%7$$\"+!4Lpl\"Fh\\m$\"+dd2KXF\\]m7$$\"+5p1VFh\\m$\"+5wPiaF\\]m7$$\"+dJC= >Fh\\m$\"+H!38Y&F\\]m7%7$$\"+Y\")oc>Fh\\m$\"+;:\")RXF\\]m7$$\"+a=JV?Fh \\m$\"+>%)=gaF\\]m7$$\"+c=J=?Fh\\m$\"+hMQgaF\\]m-Fb[m6&Fd[m$\")+++!)Fg [m$\")AR!)\\Fg[m$\")Vyg>Fg[m-%+AXESLABELSG6$%\"xG%\"yG-%%VIEWG6$;$\"*+ +++&Fe\\m$\"++++&4#Fh\\m;$!++++vJFh\\m$\"++++]nF\\]m" 2 562 362 362 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 371 16 "Linear Equations" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 270 6 "Theory" } {TEXT 390 1 "\n" }}{PARA 0 "" 0 "" {TEXT 377 76 "Suppose that we are t o solve a first order differential equation of the form" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 372 24 "y '(x) = F( x , y(x ) ). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 379 18 "If the expression" }{TEXT -1 2 " " }{TEXT 373 15 " F( x , y(x) ) " }{TEXT -1 2 " " }{TEXT 378 19 "can be expressed as" }{TEXT -1 2 " " }{TEXT 374 17 "f(x) - a(x)y(x) " }{TEXT -1 2 " " }{TEXT 380 31 "then the equation is said to be" }{TEXT -1 2 " " }{TEXT 376 6 "linear" } {TEXT -1 2 ". " }{TEXT 381 31 " It is more commonly written as" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 375 29 "y ' (x) \+ + a(x)y(x) = f(x). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 382 14 "The expression" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 29 " " }{TEXT 383 5 " " }{XPPEDIT 384 0 "exp(Int(a(x),x));" "-%$expG6#-%$IntG6$- %\"aG6#%\"xGF+" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 386 5 "is an" }{TEXT -1 1 " " }{TEXT 385 18 "integrating factor " }{TEXT -1 3 ". " }{TEXT 387 31 "The solution to the equation is" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 388 4 " " }{XPPEDIT 389 0 "y(x) = exp(-Int(a(x),x))*(Int(exp(Int(a(x),x))*f(x),x)+C);" "/-%\"yG6#%\"xG* &-%$expG6#,$-%$IntG6$-%\"aG6#F&F&!\"\"\"\"\",&-F-6$*&-F)6#-F-6$-F06#F& F&F3-%\"fG6#F&F3F&F3%\"CGF3F3" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 269 7 "Exampl e" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 391 26 "Sol ve the linear equation " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 " " }{TEXT 392 8 " " } {XPPEDIT 393 0 "diff(y(x),x)-y(x)/x = x^2*sin(x^2);" "/,&-%%diffG6$-% \"yG6#%\"xGF*\"\"\"*&-F(6#F*F+F*!\"\"F/*&F*\"\"#-%$sinG6#*$F*F1F+" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 394 9 "Solution:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "restart: with(DEtools): with (plots):" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "diff_eq := diff(y(x),x) - y(x)/x = x^2*sin(x^2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%(diff_eqG/,&-%%diffG6$-%\"yG6#%\"xGF -\"\"\"*&F*F.F-!\"\"F0*&F-\"\"#-%$sinG6#*$F-F2F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "dsolve(diff_eq, y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,&*&F'\"\"\"-%$cosG6#*$F'\"\"#F*#!\"\"F/* &F'F*%$_C1GF*F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "Code for " }{TEXT 501 11 " linear_ode" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10118 "linear_ ode := proc()\noption `Copyright \2511997-2000 Brian E. Blank, All Ri ghts Reserved.`:\nlocal xx, yy, yy2, x_0, y_0, diff_count, diff_indx, \+ expr, aa_yy, deriv, aa, yy_lhs, eqn, eqn2, Eqn3, eqn3, eqn4, cc, LIST1 , LIST2, LIST3, NF1, NF2, NF3, ii, jj, kk, nn, zz, oi, ff_xx, yy_rhs, \+ eqtns, returnList, C, _CC;\n\nif nargs < 1 or nargs > 2 then \nERROR(` linear_ode expects one or two arguments.`);\nfi:\n\nif nargs = 1 and n ot type(args[1],equation) then\nERROR(`linear_ode expects its argument to be an equation.`):\nelif nargs = 2 and (not type(args[1],equation) or not type(args[2],equation))\nthen\nERROR(`linear_ode expects its a rguments to be equations.`):\nfi:\n\nif nargs = 2 then\nif (not type( \+ lhs(args[2]),function) or not type(op(0,lhs(args[2])), name) or nops( \+ lhs(args[2]) ) <> 1 or not type(rhs(args[2]),algebraic))\nthen ERROR(` linear_ode expects its second argument to be of the form y(a) = c.`): \nelse \ny_0 := rhs(args[2]);\nx_0 := op(1,lhs(args[2])):\nyy2 := op(0 ,lhs(args[2])):\nfi:\nfi:\n\n######################################### ##########\n# #\n# The next section checks to see if the equation #\n# is of the form diff( y(x),x) = f(x)*y(x)^n #\n# If so, separable_ode will be called. \+ # \n# #\n# ##################################################\n\n###### Begin Che ck for Separability Section #####\n\nif not type(lhs(args[1]),`+`) the n\n\nif not has(lhs(args[1]), diff) then\nERROR(`linear_ode expects it s first argument to be of the form diff(y(x),x)+a(x)*y(x)=f(x)*y(x).`) :\nelif nops(op(1,lhs(args[1]))) <> 1\nthen\nERROR(`linear_ode expects its first argument to be of the form diff(y(x),x)+a(x)*y(x)=f(x)*y(x) where y(x) is a function of one variable.`):\nelif not type(op(1,(op( 1,lhs(args[1])))),name)\nthen\nERROR(`linear_ode expects its first arg ument to be of the form diff(y(x),x)+a(x)*y(x)=f(x)*y(x) where y(x) is a function of one variable and x is a name of a variable.`):\nelse\nx x := op(1,(op(1,lhs(args[1])))):\nexpr := rhs(args[1]):\nfi;\n\n\nif n ot type(rhs(args[1]), algebraic) then\nERROR(`linear_ode expects its f irst argument to be of the form diff(y(x),x)+a(x)*y(x)=f(x)*y(x).`):\n fi:\n\nif nargs = 2 and op(0,op(1,lhs(args[1])))<>yy\nthen\nERROR(`lin ear_ode expects the dependent variable names in the first two argument s to be the same.`):\nfi:\n\nif nargs = 1 then\nprintf(`Switching to t ype [separable].\\nCalling separable_ode:\\n\\n`):\nRETURN(separable_o de(args[1]));\nelse\nprintf(`Switching to type [separable].\\nCalling \+ separable_ode:\\n\\n`):\nRETURN(separable_ode(args[1],args[2]));\nfi: \n\nfi: \n\n###### End Check for Separability Section #####\n\n####### ## From here on, nops(lhs(args[1])) > 1 #########\n\nif nops(lhs(args[ 1])) > 2 then\nERROR(`linear_ode expects the left side of its first ar gument to be of the form diff(y(x),x)+a(x)*y(x).`):\nfi:\n\n########## #################################################\n# \+ #\n# The next section checks t hat diff appears exactly once #\n# on the left. The index, 1 or 2, th at it appears in is #\n# called diff_indx. \+ #\n# \+ #\n# Maple will have arranged a proper lhs #\n# \+ so that diff_indx = 2 but it can't hurt to be sure. #\n# \+ #\n##################### ######################################\n\n############# Begin diff che ck #############\n\ndiff_count := 0:\nfor jj from 1 to 2 do\nif has(op (jj,lhs(args[1])),diff) then \n diff_count := diff_count+1:\n diff_i ndx := jj:\nfi:\nod:\n\n\nif diff_count <> 1 then\nERROR(`linear_ode e xpects the left side of its first argument to be of the form diff(y(x) ,x)+a(x)*y(x).`):\nfi:\n\n\nif not has(op(diff_indx,lhs(args[1])),diff ) then\nERROR(`linear_ode expects the left side of its first argument \+ to be of the form diff(y(x),x)+a(x)*y(x).`):\nfi:\n############# End d iff check #############\n\noi := 3-diff_indx:\naa_yy := op(oi,lhs(args [1])):\nderiv := op(diff_indx,lhs(args[1])):\n\n############# Begin fi nding variables #############\n\nif nops(op(1,deriv)) <>1 or nops(op(2 ,deriv)) <> 1\nthen\nERROR(`linear_ode expects the left side of its fi rst argument to be of the form diff(y(x),x)+a(x)*y(x).`):\nelif not ty pe(op(1,op(1,deriv)),name)\nor\nnot type( op(2,deriv),name) then\nERRO R(`linear_ode expects the left side of its first argument to be of the form diff(y(x),x)+a(x)*y(x).`):\n\nelse\nxx := op(1,op(1,deriv)):\nif xx<>op(2,deriv)\nthen\nERROR(`linear_ode expects the left side of its first argument to be of the form diff(y(x),x)+a(x)*y(x).`):\nfi:\nyy \+ := op(0,op(1,deriv)):\nif nargs = 2 and yy2<>yy\nthen\nERROR(`linear_o de expects the dependent variable names in the first two arguments to \+ be the same.`):\nfi:\nfi;\n\n\nif not type(rhs(args[1]), algebraic) th en\nERROR(`linear_ode expects its first argument to be of the form dif f(y(x),x)=F(x,y(x)).`):\nfi:\n############# End finding variables #### #########\n\n\n\n\n###### Begin finding coeff of yy(xx) on lhs of ode \+ ######\n\nexpr := aa_yy:\nif type(factor(numer(expr)),`*`) then\n L IST1 := [op(factor(numer(expr)))];\nelse\n LIST1 := [numer(expr)]; \nfi;\nif type(denom(expr),`*`) then\n LIST2 := map(z->z^(-1),[op(fa ctor(denom(expr)))]);\nelse\n LIST2 := [denom(expr)^(-1)];\nfi;\nNF 1 := nops(LIST1);\nNF2 := nops(LIST2); \nLIST3 := [];\nfor kk from 1 t o NF1 do\nif type(LIST1[kk], `^`) and nops(op(1,LIST1[kk])) > 1 and ty pe(op(1,LIST1[kk]),`*`) then\n for jj from 1 to nops(op(1,LIST1[kk]) ) do\n LIST3 := [op(LIST3),op(jj,op(1,LIST1[kk]))^op(2,LIST1[kk])]; \n od;\nelse\nLIST3 := [op(LIST3),LIST1[kk]];\nfi;\nod; \n\nfor kk f rom 1 to NF2 do\nif type(LIST2[kk], `^`) and nops(op(1,LIST2[kk])) > 1 and type(op(1,LIST2[kk]),`*`) then\n for jj from 1 to nops(op(1,LIS T2[kk])) do\n LIST3 := [op(LIST3),op(jj,op(1,LIST2[kk]))^(-op(2,LIST 2[kk]))];\n od:\nelse\nLIST3 := [op(LIST3),LIST2[kk]];\nfi;\nod;\n\n NF3 := nops(LIST3);\n\naa := 1:\nyy_lhs := 1:\n\nfor jj from 1 to NF3 \+ do\nif has(LIST3[jj],yy(xx) ) \n then yy_lhs := yy_lhs*LIST3[jj];\ne lse\n aa := aa*LIST3[jj];\nfi;\nod;\n\n\n\n\nif yy_lhs <> yy(xx)\nth en\nERROR(`linear_ode expects the left side of its first argument to b e of the type diff(y(x),x)+a(x)*y(x).`);\nfi:\n###### End finding coef f of yy(xx) on lhs of ode ######\n\n\n############# Begin checking rhs of ode #############\nexpr := factor(rhs(args[1])):\n\nif type(factor (numer(expr)),`*`) then\n LIST1 := [op(factor(numer(expr)))];\nelse \n LIST1 := [numer(expr)];\nfi;\nif type(denom(expr),`*`) then\n \+ LIST2 := map(z->z^(-1),[op(factor(denom(expr)))]);\nelse\n LIST2 := [denom(expr)^(-1)];\nfi;\nNF1 := nops(LIST1);\nNF2 := nops(LIST2); \n LIST3 := [];\nfor kk from 1 to NF1 do\nif type(LIST1[kk], `^`) and nop s(op(1,LIST1[kk])) > 1 and type(op(1,LIST1[kk]),`*`) then\n for jj f rom 1 to nops(op(1,LIST1[kk])) do\n LIST3 := [op(LIST3),op(jj,op(1,L IST1[kk]))^op(2,LIST1[kk])];\n od;\nelse\nLIST3 := [op(LIST3),LIST1[ kk]];\nfi;\nod; \n\nfor kk from 1 to NF2 do\nif type(LIST2[kk], `^`) a nd nops(op(1,LIST2[kk])) > 1 and type(op(1,LIST2[kk]),`*`) then\n fo r jj from 1 to nops(op(1,LIST2[kk])) do\n LIST3 := [op(LIST3),op(jj, op(1,LIST2[kk]))^(-op(2,LIST2[kk]))];\n od:\nelse\nLIST3 := [op(LIST 3),LIST2[kk]];\nfi;\nod;\n\nNF3 := nops(LIST3);\n\nff_xx := 1:\nyy_rhs := 1:\n\nfor jj from 1 to NF3 do\nif has(LIST3[jj],yy(xx) ) \n then yy_rhs := yy_rhs*LIST3[jj];\nelse\n ff_xx := ff_xx*LIST3[jj];\nfi; \nod;\n\n\n\nif has(ff_xx,yy) then\nERROR(`The first argument passed t o linear_ode does not appear to be a differential equation of linear t ype.`):\nfi:\n\nnn := simplify(log[2](subs(yy(xx)=2,yy_rhs))):\nif yy_ rhs <> yy(xx)^nn then \nERROR(`The first argument passed to linear_ode does not appear to be a linear differential equation.`):\nfi:\n###### ####### End checking rhs of ode #############\n\n\n\n\n\n\n\n######### ##########################################\n# \+ #\n# The next section checks to see if the equ ation #\n# is of the form diff(y(x),x)+a(x)*y(x)=f(x)*y(x) #\n# If so , separable_ode(\{args\}) will be called. # \n# \+ #\n###################################### #############\n\n\n###### Begin Check for Separability Section #####\n \nif nn = 1 then \nprintf(`Equation is separable. Switching to type s eparable:\\n`);\nif nargs = 2 then\nRETURN( [args[1],op(separable_ode( \{diff(yy(xx),xx)=(ff_xx-aa)*yy(xx),args[2]\}))]);\nelse\nRETURN([args [1],op(separable_ode(diff(yy(xx),xx)=(ff_xx-aa)*yy(xx)))]);\nfi: \nfi: \n###### End Check for Separability Section #####\n\nif nn <> 0 then\n ERROR(`linear_ode expects its first argument to be of the form diff(y( x),x)+a(x)*y(x)=f(x) but received diff(y(x),x)+a(x)*y(x)=f(x)*y(x)^n w ith n<>0 instead. Use Bernoulli_ode.`);\nfi:\n\n###### Now we are in t rue Linear case #####\nreturnList := []:\nif nargs = 1 then\nreturnLis t := [op(returnList),args[1]]:\nreturnList := [op(returnList),exp(Int( aa,xx))*args[1]]:\nreturnList := [op(returnList), Diff(`(`*exp(Int(aa, xx))*yy(xx)*`)`,xx)=exp(Int(aa,xx))*ff_xx]:\nreturnList := [op(returnL ist),\nexp(Int(aa,xx))*yy(xx)=Int(exp(Int(aa,xx))*ff_xx,xx)+_C];\nretu rnList := [op(returnList),\nexp(int(aa,xx))*yy(xx)=Int(exp(int(aa,xx)) *ff_xx,xx)+_C];\nreturnList := [op(returnList), exp(int(aa,xx))*yy(xx) =int(exp(int(aa,xx))*ff_xx,xx)+_C];\nreturnList := [op(returnList), yy (xx)=exp(-int(aa,xx))*(int(exp(int(aa,xx))*ff_xx,xx)+_C)];\nRETURN(ret urnList);\n\nelse\nreturnList := [op(returnList),args[1]]:\nreturnList := [op(returnList),exp(Int(aa,xx))*args[1]]:\nreturnList := [op(retur nList), Diff(`(`*exp(Int(aa,xx))*yy(xx)*`)`,xx)=exp(Int(aa,xx))*ff_xx] :\nreturnList := [op(returnList),\nexp(Int(aa,xx))*yy(xx)=Int(exp(Int( aa,xx))*ff_xx,xx)+C];\nreturnList := [op(returnList),\nexp(int(aa,xx)) *yy(xx)=Int(exp(int(aa,xx))*ff_xx,xx)+C];\nreturnList := [op(returnLis t), exp(int(aa,xx))*yy(xx)=int(exp(int(aa,xx))*ff_xx,xx)+C];\nreturnLi st := [op(returnList), yy(xx)=exp(-int(aa,xx))*(int(exp(int(aa,xx))*ff _xx,xx)+C)];\nreturnList := [op(returnList), yy(xx)=exp(-int(subs(xx=x i,aa),xi=x_0..xx))*(int(exp(int(subs(xx=xi,aa),xi=x_0..xx))*subs(xx=xi ,ff_xx),xi=x_0..xx)+y_0*exp(int(subs(xx=xi,aa),xi=x_0..xx)))];\nRETURN (returnList);\nfi:\nend:" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 395 8 "Gra phics" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 396 97 "In this subsection we will plot a solution curve and superimpose it o n the direction field plot. " }}{PARA 0 "" 0 "" {TEXT -1 36 "\nRemembe r the differential equation:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "di ff_eq := diff(y(x),x) - y(x)/x = x^2*sin(x^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(diff_eqG/,&-%%diffG6$-%\"yG6#%\"xGF-\"\"\"*&F*F.F-! \"\"F0*&F-\"\"#-%$sinG6#*$F-F2F." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 184 "The solution is the last entry of this l ist. In order to pick out that last entry we first execute the next fu nction. (It is not a built-in and must be re-executed after each resta rt.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 201 "lastEntry := proc()\n if nargs = 1 and t ype(args[1], list) then\n RETURN( args[1][nops(args[1])] ) ;\n else\n RETURN(args);\n fi:\n \+ end:" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 20 "linear_ode(diff_eq);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7)/,&-%%diffG6$-%\"yG6#%\"xGF,\"\"\"*&F)F-F,!\"\"F/*&F, \"\"#-%$sinG6#*$F,F1F-/*&-%$expG6#-%$IntG6$,$*$F,F/F/F,F-F%F-*(F8F-F,F 1F2F-/-%%DiffG6$**%\"(GF-F8F-F)F-%\")GF-F,F@/*&F8F-F)F-,&-F<6$F@F,F-%# _CGF-/F.,&-F<6$*&F,F-F2F-F,F-FMF-/F.,&-%$cosGF4#F/F1FMF-/F)*&F,F-FTF- " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "soln := lastEntry(\");" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solnG/-%\"yG6#%\"xG*&F)\"\"\",&-%$c osG6#*$F)\"\"##!\"\"F1%#_CGF+F+" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 36 "Let us impose an initial condition:\n" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "soln := subs( _C = 1, soln); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solnG/-%\"yG6#%\"xG*&F)\"\"\",& -%$cosG6#*$F)\"\"##!\"\"F1F+F+F+" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "direction_field_plot := dfieldplot( [diff_eq] , [y(x)], x = 1/2 . . 5 , y = -1.1 .. 6.8 ,color = COLOR(RGB,0.7,0.85,0.75)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "display(direction_field_plot);" }} {PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6]dl7%7$$\"+\\P_;Q!#5$!+=*>t5\" !\"*7$$\"+^iZ$='F*$!+#3!o#4\"F-7$$\"+p?fgcF*$!+U#3R/\"F-7%7$$\"+RS/*>' F*$!+3@!G8\"F-7$$\"+n!)zP&)F*$!+#*y>n5F-7$$\"+/6t%)zF*$!+j*y+.\"F-7%7$ $\"+pCQ_')F*$!+xQ^$=\"F-7$$\"+u,8#3\"F-$!+Bh[;5F-7$$\"+&*)yK-\"F-$!+kH 005F-7%7$$\"+)y1%>6F-$!+&)GyK7F-7$$\"+Wek,8F-$!+]6\"F-7$$\"+V3v!z\"F-$!+$*3C 45F-7$$\"+wHpJ%3+#F-$! +_2i`7F-7$$\"+J&o\"))>F-$!+sB3_6F-7%7$$\"+l=1;@F-$!+M()3b!*F*7$$\"+2ws *>#F-$!+F6\\%H\"F-7$$\"+k*4$4AF-$!+;S\">>\"F-7%7$$\"+*RuZL#F-$!+gZE2#* F*7$$\"+$G*paCF-$!+CNFz7F-7$$\"+TUEaCF-$!+h*G`<\"F-7%7$$\"+ZJT&e#F-$!+ \\iW\"H\"F-7$$\"+XZuxEF-$!+9v`&3*F*7$$\"+_9\\IEF-$!+Bv!>r*F*7%7$$\"+)* \\'>%GF-$!+l-k-8F-7$$\"+/r([*GF-$!+_tft*)F*7$$\"+(HkX&GF-$!+gF%\\t*F*7 %7$$\"+?k(*GIF-$!+33!*4%*F*7$$\"+#*)\\:=$F-$!+>*4!f7F-7$$\"+%eg6<$F-$! +._nc6F-7%7$$\"+*HVMK$F-$!+?)Hq%*)F*7$$\"+BswgLF-$!+=qH08F-7$$\"+\"p@> Q$F-$!+u-@37F-7%7$$\"+3WC?NF-$!+[Ob!G\"F-7$$\"+C.lPOF-$!+BNY%>*F*7$$\" +W%>le$F-$!+!*Hk=(*F*7%7$$\"+xcE+QF-$!+32518F-7$$\"+lKJJQF-$!+;H**Q*)F *7$$\"+\"[T_z$F-$!+bHIj(*F*7%7$$\"+]VfLSF-$!+&*>4[*)F*7$$\"+-)o;2%F-$! +,3>08F-7$$\"+]ck#4%F-$!+^`)z?\"F-7%7$$\"+G!*4kUF-$!+'\\R$p*)F*7$$\"+M $[[J%F-$!+]g1.8F-7$$\"+@%yFL%F-$!+<#**R?\"F-7%7$$\"+nF=;XF-$!+`A828F-7 $$\"+0)[k`%F-$!+ounG*)F*7$$\"+(RkD]%F-$!+SP6\"y*F*7%7$$\"+nw(*[ZF-$!++ 6,O*)F*7$$\"+:\"Qtx%F-$!+!*))R18F-7$$\"+X,f+[F-$!+1?!3@\"F-7%7$$\"+?u \\W\\F-$!+rO`j\"*F*7$$\"+sD]b]F-$!+Lmk$G\"F-7$$\"+i9id]F-$!+Wewz6F-7%7 $F($!+TWI:pF*7$F/$!+&31*onF*7$F4$!+#o(=\"G'F*7%7$F:$!+Rj7qrF*7$F?$!+(= %39lF*7$FD$!+,\\*G9'F*7%7$FJ$!+OSCxwF*7$FO$!+!\\mp+'F*7$FT$!+,\\j#*eF* 7%7$FZ$!+8T$*p\")F*7$Fin$!+8kF9bF*7$F^o$!+)oH$*o&F*7%7$Fdo$!+%3(*eL)F* 7$Fio$!+UMJ[`F*7$F^p$!+()3nLcF*7%7$Fdp$!+Ojp\\xF*7$Fip$!+!>9X$fF*7$F^q $!+R!>*feF*7%7$Fdq$!+Xx*eI&F*7$Fiq$!+\"y7$y$)F*7$F^r$!+z*GHO(F*7%7$Fdr $!+(*R>(*[F*7$Fir$!+Hl,(y)F*7$F^s$!+AaChxF*7%7$Fds$!+B+P\\]F*7$Fis$!+. 0%[j)F*7$F^t$!+w[R&f(F*7%7$Fdt$!+\\xcc()F*7$Fit$!+xFkF\\F*7$F^u$!+'y7S b&F*7%7$Fdu$!+6z]o))F*7$Fiu$!+:Eq:[F*7$F^v$!+B![qd&F*7%7$Fdv$!+rg+__F* 7$Fiv$!+bW?K%)F*7$F^w$!+*Hd)3uF*7%7$Fdw$!+$3N\"*y%F*7$Fiw$!+Va2&*))F*7 $F^x$!+**z?CzF*7%7$Fdx$!+S!z%F*7$Fi z$!+oK,%*))F*7$F^[l$!+r(e>#zF*7%7$Fd[l$!+fZW6[F*7$Fi[l$!+ndws))F*7$F^ \\l$!+Tu4#)yF*7%7$Fd\\l$!+&zFM\"*)F*7$Fi\\l$!+JFyqZF*7$F^]l$!+.!>Ki&F* 7%7$Fd]l$!+jj6yZF*7$Fi]l$!+jT41*)F*7$F^^l$!+C`7]zF*7%7$Fd^l$!+M*Qc+&F* 7$Fi^l$!+#fr&y')F*7$F^_l$!+/PwRwF*7%7$F($!+/(4uv#F*7$F/$!+[8,6EF*7$F4$ !+XHHB@F*7%7$F:$!+-;B7IF*7$F?$!+]%*=cBF*7$FD$!+k,+&)>F*7%7$FJ$!+*H\\$> NF*7$FO$!+`<2\\=F*7$FT$!+k,uM\"F*7$F^p$!+]hxv9F*7%7$Fdp$!+* f,=f$F*7$Fip$!+`%>mx\"F*7$F^q$!+-V--9F*7%7$Fdv$!+M86%4\"F*7$Fiv$!+=(4VF%F*7$F^w$!+iD'4D$F*7%7$Fdw$!*Y .CJ'F*7$Fiw$!+12=PZF*7$F^x$!+iKJmPF*7%7$Fdx$!+.qu*[%F*7$Fix$!*\\Sny)F* 7$F^y$!+;N&GS\"F*7%7$Fdy$!+5w@XZF*7$Fiy$!*UM?B'F*7$F^z$!+\"[8vW\"F*7%7 $Fdz$!*@DIK'F*7$Fiz$!+J&=ht%F*7$F^[l$!+MS1kPF*7%7$Fd[l$!*A+b`'F*7$Fi[l $!+I5([r%F*7$F^\\l$!+/F?CPF*7%7$Fd\\l$!+eI`bZF*7$Fi\\l$!*%*z)GhF*7$F^] l$!+mUKl9F*7%7$Fd]l$!*E;A?'F*7$Fi]l$!+E%*>[ZF*7$F^^l$!+(eIAz$F*7%7$Fd^ l$!*(>Wx%)F*7$Fi^l$!+bon?XF*7$F^_l$!+n*o=[$F*7%7$F($\"+L][+9F*7$F/$\"+ *Q$)oa\"F*7$F4$\"+#z,Y.#F*7%7$F:$\"+NJmX6F*7$F?$\"+(G0kE$F*7$Fis$!*H50>$F*7$F^t$ \"*)f%R?(F*7%7$Fdt$!*v#y2WF*7$Fit$\"+(pY\")Q$F*7$F^u$\"+)ow'F*7%7$F:$\"+syb.`F*7$F?$\"+C+gffF*7$FD$\"+5$*yIjF*7%7$ FJ$\"+v,W'z%F*7$FO$\"+@xrmkF*7$FT$\"+5$\\5e'F*7%7$FZ$\"+)4]PI%F*7$Fin$ \"+)z2%fpF*7$F^o$\"+CXN%y'F*7%7$Fdo$\"+FryPTF*7$Fio$\"+p2PDrF*7$F^p$\" +CL,SoF*7%7$Fdp$\"+vy)Rs%F*7$Fip$\"+@+pF*7%7$Fdu$\"++j< 0OF*7$Fiu$\"+'f\")zl(F*7$F^v$\"+)=Om*oF*7%7$Fdv$\"+S\"y;A(F*7$Fiv$\"+c (z9/%F*7$F^w$\"+7p#[1&F*7%7$Fdw$\"+G\"\\Xo(F*7$Fiw$\"+o(3'yNF*7$F^x$\" +7iZ\\XF*7%7$Fdx$\"+rC/EQF*7$Fix$\"+Da6PuF*7$F^y$\"+ef$H\"pF*7%7$Fdy$ \"+k=dqNF*7$Fiy$\"+Kge#p(F*7$F^z$\"+$*fFooF*7%7$Fdz$\"+`p[$o(F*7$Fiz$ \"+V4nzNF*7$F^[l$\"+Sas^XF*7%7$Fd[l$\"+_%RAm(F*7$Fi[l$\"+W%=4g$F*7$F^ \\l$\"+qne\"f%F*7%7$Fd\\l$\"+;kDgNF*7$Fi\\l$\"+![,Hq(F*7$F^]l$\"+4_Y]o F*7%7$Fd]l$\"+[yc&p(F*7$Fi]l$\"+[+fnNF*7$F^^l$\"+())eN_%F*7%7$Fd^l$\"+ x_/ouF*7$Fi^l$\"+>E6&z$F*7$F^_l$\"+20#R$[F*7%7$F($\"+2XF;(*F*7$F/$\"+j Gni)*F*7$F4$\"+F\"R].\"F-7%7$F:$\"+4EXh%*F*7$F?$\"+w%\\<,\"F-7$FD$\"+0 %o)[5F-7%7$FJ$\"+7\\La*)F*7$FO$\"+Y7Yi5F-7$FT$\"+0W*Q2\"F-7%7$FZ$\"+N[ kh%)F*7$Fin$\"+a-t66F-7$F^o$\"+F\\A%4\"F-7%7$Fdo$\"+k=o&H)F*7$Fio$\"+^ lKG6F-7$F^p$\"+13z*4\"F-7%7$Fdp$\"+7E)=)))F*7$Fip$\"+wkqp5F-7$F^q$\"+ \"*f;x5F-7%7$Fdq$\"+?\"oD8\"F-7$Fiq$\"+nhE`#)F*7$F^r$\"+p*\\'o#*F*7%7$ Fdr$\"+&\\QM<\"F-7$Fir$\"+>CcWyF*7$F^s$\"+ENLq))F*7%7$Fds$\"+$*3Ae6F-7 $Fis$\"+X%Qn*zF*7$F^t$\"+sS=O!*F*7%7$Fdt$\"+*>6](yF*7$Fit$\"+)F*7$F^w$\"+\\;sA#*F*7%7$Fdw$\"+(QW U=\"F-7$Fiw$\"+0N]OxF*7$F^x$\"+\\4P2()F*7%7$Fdx$\"+3s$R)zF*7$Fix$\"+;5 ]f6F-7$F^y$\"+pI326F-7%7$Fdy$\"+,mYGxF*7$Fiy$\"+x![]=\"F-7$F^z$\"+tqh- 6F-7%7$Fdz$\"+p\"QT=\"F-7$Fiz$\"+!olvt(F*7$F^[l$\"+x,i4()F*7%7$Fd[l$\" +>M,#=\"F-7$Fi[l$\"+\"=8)exF*7$F^\\l$\"+2:[\\()F*7%7$Fd\\l$\"+`6:=xF*7 $Fi\\l$\"+A'zg=\"F-7$F^]l$\"+&*f$35\"F-7%7$Fd]l$\"+fiM&=\"F-7$Fi]l$\"+ &y%[DxF*7$F^^l$\"+COX\"o)F*7%7$Fd^l$\"+,Sfi6F-7$Fi^l$\"+ct+`zF*7$F^_l$ \"+W_\"=**)F*7%7$F($\"+CpT(Q\"F-7$F/$\"+gn0-9F-7$F4$\"++'G3X\"F-7%7$F: $\"+MZ$>O\"F-7$F?$\"+]*QvU\"F-7$FD$\"+zylk9F-7%7$FJ$\"+lHA68F-7$FO$\"+ >2Dy9F-7$FT$\"+yQo*[\"F-7%7$FZ$\"+dR&>E\"F-7$Fin$\"+F(>v_\"F-7$F^o$\"+ +W,5:F-7%7$Fdo$\"+gwNX7F-7$Fio$\"+Cg6W:F-7$F^p$\"+z-e::F-7%7$Fdp$\"+Nx (RI\"F-7$Fip$\"+\\f\\&[\"F-7$F^q$\"+ka&H\\\"F-7%7$Fdq$\"+%fd$[:F-7$Fiq $\"+!4;6C\"F-7$F^r$\"+qWlU8F-7%7$Fdr$\"+pzA*e\"F-7$Fir$\"+:dC+7F-7$F^s $\"+EG#GI\"F-7%7$Fds$\"+m.,u:F-7$Fis$\"+=LY:7F-7$F^t$\"+\")yS>8F-7%7$F dt$\"+$f!H.7F-7$Fit$\"+\"4$='e\"F-7$F^u$\"+!4YN_\"F-7%7$Fdu$\"+xl4#>\" F-7$Fiu$\"+2rP(f\"F-7$F^v$\"+mDC@:F-7%7$Fdv$\"+hnu`:F-7$Fiv$\"+BpsN7F- 7$F^w$\"+R;1Q8F-7%7$Fdw$\"+gQ.+;F-7$Fiw$\"+C)R%*=\"F-7$F^x$\"+ol_'G\"F -7%7$Fdx$\"+%>$=97F-7$Fix$\"+!\\!Hv:F-7$F^y$\"+VD(G_\"F-7%7$Fdy$\"+Mhj )=\"F-7$Fiy$\"+]v$3g\"F-7$F^z$\"+YlS=:F-7%7$Fdz$\"+Vw#**f\"F-7$Fiz$\"+ Uga*=\"F-7$F^[l$\"+#\\^nG\"F-7%7$Fd[l$\"+#*G!yf\"F-7$Fi[l$\"+#zq;>\"F- 7$F^\\l$\"+Dwt!H\"F-7%7$Fd\\l$\"+*e/w=\"F-7$Fi\\l$\"+&4p=g\"F-7$F^]l$ \"+oai;:F-7%7$Fd]l$\"+Kd8,;F-7$Fi]l$\"+_zL)=\"F-7$F^^l$\"+O[$RG\"F-7%7 $Fd^l$\"+vMQy:F-7$Fi^l$\"+4-467F-7$F^_l$\"+)*4(\\J\"F-7%7$F($\"+)R1K!= F-7$F/$\"+Mi%y\"=F-7$F4$\"+u!=m'=F-7%7$F:$\"+3UsxSS*=F-7$FT$\"+_LZ0>F-7%7$FZ$ \"+JMux;F-7$Fin$\"+,#4L%>F-7$F^o$\"+uQ!e#>F-7%7$Fdo$\"+Mr9h;F-7$Fio$\" +)\\0*f>F-7$F^p$\"+`(p8$>F-7%7$Fdp$\"+4sw>F-7$F^q$\"+ Q\\u3>F-7%7$Fdq$\"+oq9k>F-7$Fiq$\"+kb!pl\"F-7$F^r$\"+WRWeF-7$Fis$\" +#z_7j\"F-7$F^t$\"+bt>N;F-7$Fit$\"+lD(>+#F-7$F^u$\"+ kbLR>F-7%7$Fdu$\"+^g)yg\"F-7$Fiu$\"+\"emJ,#F-7$F^v$\"+S?.P>F-7%7$Fdv$ \"+Ni`p>F-7$Fiv$\"+(R;:l\"F-7$F^w$\"+86&Qv\"F-7%7$Fdw$\"+ML#e,#F-7$Fiw $\"+)HH_g\"F-7$F^x$\"+UgJ-F-7$F^y $\"+F-7%7$Fdy$\"+3cU/;F-7$Fiy$\"+Cqi;?F-7$F^z$\"+?g>M>F-7%7$Fdz$ \"+F-7%7$Fd]l$\"+1_#p,#F-7$Fi]l$\"+Eu7/;F-7$F^^l$\"+5Vs*p \"F-7%7$Fd^l$\"+\\H<%*>F-7$Fi^l$\"+$ozoi\"F-7$F^_l$\"+s/wI#F-7$F?$\"+)*y6 fAF-7$FD$\"+FoB'H#F-7%7$FJ$\"+8>!G9#F-7$FO$\"+n'H)4BF-7$FT$\"+EGE@BF-7 %7$FZ$\"+0H`$4#F-7$Fin$\"+v')4fBF-7$F^o$\"+[LfTBF-7%7$Fdo$\"+3m$p2#F-7 $Fio$\"+s\\pvBF-7$F^p$\"+F#frM#F-7%7$Fdp$\"+$ocb8#F-7$Fip$\"+(*[2?F-7$Fi\\l$\"+ V![MV#F-7$F^]l$\"+;W?[BF-7%7$Fd]l$\"+!o9FV#F-7$Fi]l$\"++p\"*>?F-7$F^^l $\"+%y8b6#F-7%7$Fd^l$\"+BC'*4CF-7$Fi^l$\"+d\"pE/#F-7$F^_l$\"+Y*\\l9#F- 7%7$F($\"+Y`yMEF-7$F/$\"+#=D%\\EF-7$F4$\"+Aq>)p#F-7%7$F:$\"+cJI4EF-7$F ?$\"+st!\\n#F-7$FD$\"+,j-7FF-7%7$FJ$\"+(Q\"feDF-7$FO$\"+T\">cs#F-7$FT$ \"++B0PFF-7%7$FZ$\"+zBK4DF-7$Fin$\"+\\\"))[x#F-7$F^o$\"+AGQdFF-7%7$Fdo $\"+#3EF\\#F-7$Fio$\"+YW[\"z#F-7$F^p$\"+,([Hw#F-7%7$Fdp$\"+dhM^DF-7$Fi p$\"+rV'Gt#F-7$F^q$\"+')QKSFF-7%7$Fdq$\"+;gs&z#F-7$Fiq$\"+7X[)[#F-7$F^ r$\"+#*G-!f#F-7%7$Fdr$\"+\"R'fOGF-7$Fir$\"+PThZCF-7$F^s$\"+[7>]DF-7%7$ Fds$\"+)yy8#GF-7$Fis$\"+S<$GY#F-7$F^t$\"+.jxmDF-7%7$Fdt$\"+:!f1X#F-7$F it$\"+8:bLGF-7$F^u$\"+7X\"4x#F-7%7$Fdu$\"+**\\YRCF-7$Fiu$\"+HbuWGF-7$F ^v$\"+))4hoFF-7%7$Fdv$\"+$=:6!GF-7$Fiv$\"+X`4$[#F-7$F^w$\"+h+V&e#F-7%7 $Fdw$\"+#G-u%GF-7$Fiw$\"+Y#3oV#F-7$F^x$\"+!*\\*Q`#F-7%7$Fdx$\"+;;bhCF- 7$Fix$\"+7*eE#GF-7$F^y$\"+l4CqFF-7%7$Fdy$\"+cX+OCF-7$Fiy$\"+sf?[GF-7$F ^z$\"+o\\xlFF-7%7$Fdz$\"+lgHZGF-7$Fiz$\"+kW\"pV#F-7$F^[l$\"+9*>T`#F-7% 7$Fd[l$\"+98$F-7$F^o$\"+'HsJ< $F-7%7$Fdo$\"+cb^3HF-7$Fio$\"+?RF2KF-7$F^p$\"+v\"Q(yJF-7%7$Fdp$\"+Jc8n HF-7$Fip$\"+XQl[JF-7$F^q$\"+gL6cJF-7%7$Fdq$\"+!\\::@$F-7$Fiq$\"+')RF/H F-7$F^r$\"+mB\"e+$F-7%7$Fdr$\"+leQ_KF-7$Fir$\"+6OSjGF-7$F^s$\"+A2)f'HF -7%7$Fds$\"+i#orB$F-7$Fis$\"+97iyGF-7$F^t$\"+xdc#)HF-7%7$Fdt$\"+*[[k'G F-7$Fit$\"+()4M\\KF-7$F^u$\"+')Rq'=$F-7%7$Fdu$\"+tWDbGF-7$Fiu$\"+.]`gK F-7$F^v$\"+i/S%=$F-7%7$Fdv$\"+dY!p@$F-7$Fiv$\"+>[)))*GF-7$F^w$\"+N&>7+ $F-7%7$Fdw$\"+c<>jKF-7$Fiw$\"+?xf_GF-7$F^x$\"+kWo\\HF-7%7$Fdx$\"+!4Tt( GF-7$Fix$\"+'Q[%QKF-7$F^y$\"+R/.'=$F-7%7$Fdy$\"+ISz^GF-7$Fiy$\"+Ya*RE$ F-7$F^z$\"+UWc\"=$F-7%7$Fdz$\"+Rb3jKF-7$Fiz$\"+QRq_GF-7$F^[l$\"+)Q4*\\ HF-7%7$Fd[l$\"+)yg4E$F-7$Fi[l$\"+)oG[&GF-7$F^\\l$\"+@b*Q&HF-7%7$Fd\\l$ \"+&[i2&GF-7$Fi\\l$\"+\"*p-lKF-7$F^]l$\"+kLyzJF-7%7$Fd]l$\"+GOHkKF-7$F i]l$\"+[e\\^GF-7$F^^l$\"+KF4ZHF-7%7$Fd^l$\"+r8aTKF-7$Fi^l$\"+0\"[U(GF- 7$F^_l$\"+%*)G\"yHF-7%7$F($\"+%HkjY$F-7$F/$\"+IT+\"[$F-7$F4$\"+qfxHNF- 7%7$F:$\"+/@)3W$F-7$F?$\"+?j[1NF-7$FD$\"+\\_gVNF-7%7$FJ$\"+N.dNF-7$FT$\"+[7joNF-7%7$FZ$\"+F8!4M$F-7$Fin$\"+(4nkg$F-7$F^o$ \"+q<'*)e$F-7%7$Fdo$\"+I]ICLF-7$Fio$\"+%RjIi$F-7$F^p$\"+\\w_%f$F-7%7$F dp$\"+0^#HQ$F-7$Fip$\"+>LWkNF-7$F^q$\"+MG!>d$F-7%7$Fdq$\"+k\\IFOF-7$Fi q$\"+gM1?LF-7$F^r$\"+S=g@MF-7%7$Fdr$\"+R`zKF-7$F^s$ \"+'>q(QoKF-7$F^x$\"+QRZlLF-7%7$Fdx$ \"+k08$H$F-7$Fix$\"+gyBaOF-7$F^y$\"+8*>=g$F-7%7$Fdy$\"+/NenKF-7$Fiy$\" +?\\yzOF-7$F^z$\"+;RN(f$F-7%7$Fdz$\"+8]()yOF-7$Fiz$\"+7M\\oKF-7$F^[l$ \"+i))plLF-7%7$Fd[l$\"+i-vwOF-7$Fi[l$\"+i\"=1F$F-7$F^\\l$\"+&*\\opLF-7 %7$Fd\\l$\"+f>bmKF-7$Fi\\l$\"+lk\"3o$F-7$F^]l$\"+QGd&f$F-7%7$Fd]l$\"+- J3!o$F-7$Fi]l$\"+A`GnKF-7$F^^l$\"+1A)GO$F-7%7$Fd^l$\"+X3LdOF-7$Fi^l$\" +zv.!H$F-7$F^_l$\"+o$=RR$F-7%7$F($\"+oP:#)QF-7$F/$\"+/Oz'*QF-7$F4$\"+W acXRF-7%7$F:$\"+y:ncQF-7$F?$\"+%zvA#RF-7$FD$\"+BZRfRF-7%7$FJ$\"+4)ff!Q F-7$FO$\"+jv)H(RF-7$FT$\"+A2U%)RF-7%7$FZ$\"+,3pcPF-7$Fin$\"+rlDASF-7$F ^o$\"+W7v/SF-7%7$Fdo$\"+/X4SPF-7$Fio$\"+oG&)QSF-7$F^p$\"+BrJ5SF-7%7$Fd p$\"+zXr)z$F-7$Fip$\"+$zK-)RF-7$F^q$\"+3Bp()RF-7%7$Fdq$\"+QW4VSF-7$Fiq $\"+MH&et$F-7$F^r$\"+98RPQF-7%7$Fdr$\"+8['R3%F-7$Fir$\"+fD)\\p$F-7$F^s $\"+q'fvz$F-7%7$Fds$\"+5suoSF-7$Fis$\"+i,?5PF-7$F^t$\"+DZ99QF-7%7$Fdt$ \"+Pu-)p$F-7$Fit$\"+N*>43%F-7$F^u$\"+MHG=SF-7%7$Fdu$\"+@M$oo$F-7$Fiu$ \"+^R6#4%F-7$F^v$\"+5%zf,%F-7%7$Fdv$\"+0O[[SF-7$Fiv$\"+nPYIPF-7$F^w$\" +$[)zKQF-7%7$Fdw$\"+/2x%4%F-7$Fiw$\"+om<%o$F-7$F^x$\"+7ME\"y$F-7%7$Fdx $\"+Q+#*3PF-7$Fix$\"+Mt-qSF-7$F^y$\"+(Q4w,%F-7%7$Fdy$\"+yHP$o$F-7$Fiy$ \"+%Rub4%F-7$F^z$\"+!RVJ,%F-7%7$Fdz$\"+([kY4%F-7$Fiz$\"+')GG%o$F-7$F^[ l$\"+O$)[\"y$F-7%7$Fd[l$\"+O(RD4%F-7$Fi[l$\"+OwS'o$F-7$F^\\l$\"+pWZ&y$ F-7%7$Fd\\l$\"+L9M#o$F-7$Fi\\l$\"+Rfg'4%F-7$F^]l$\"+7BO6SF-7%7$Fd]l$\" +wD(e4%F-7$Fi]l$\"+'zuIo$F-7$F^^l$\"+!or'yPF-7%7$Fd^l$\"+>.7tSF-7$Fi^l $\"+`q#eq$F-7$F^_l$\"+Uyq4QF-7%7$F($\"+UK%zH%F-7$F/$\"+yIe7VF-7$F4$\"+ =\\NhVF-7%7$F:$\"+_5YsUF-7$F?$\"+o_1QVF-7$FD$\"+(>%=vVF-7%7$FJ$\"+$G\\ 5-S%F-7%7$FZ$\"+v-[sTF-7$Fin$\"+Xg/QWF- 7$F^o$\"+=2a?WF-7%7$Fdo$\"+yR)e:%F-7$Fio$\"+UBkaWF-7$F^p$\"+(f1hU%F-7% 7$Fdp$\"+`S]9UF-7$Fip$\"+nA-'R%F-7$F^q$\"+#y\"[.WF-7%7$Fdq$\"+7R))eWF- 7$Fiq$\"+3Ck^TF-7$F^r$\"+)y!=`UF-7%7$Fdr$\"+(Ga(*\\%F-7$Fir$\"+L?x5TF- 7$F^s$\"+W\"\\L@%F-7%7$Fds$\"+%oOX[%F-7$Fis$\"+O'*)f7%F-7$F^t$\"+*>M*H UF-7%7$Fdt$\"+6p\"Q6%F-7$Fit$\"+4%4n\\%F-7$F^u$\"+3C2MWF-7%7$Fdu$\"+&* Gi-TF-7$Fiu$\"+DM!z]%F-7$F^v$\"+%))o%F-7%7$Fdx$\"+7&4Z7%F-7$Fix$\"+3o\"e[%F-7$F^y$\"+h))RLWF-7%7$Fdy$\"+ _C;*4%F-7$Fiy$\"+oQO6XF-7$F^z$\"+kG$*GWF-7%7$Fdz$\"+hRX5XF-7$Fiz$\"+gB 2+TF-7$F^[l$\"+5yF(>%F-7%7$Fd[l$\"+5#H$3XF-7$Fi[l$\"+5r>-TF-7$F^\\l$\" +VRE,UF-7%7$Fd\\l$\"+248)4%F-7$Fi\\l$\"+8aR7XF-7$F^]l$\"+'y^rU%F-7%7$F d]l$\"+]?m6XF-7$Fi]l$\"+qU'))4%F-7$F^^l$\"+a6Y%>%F-7%7$Fd^l$\"+$z4*)[% F-7$Fi^l$\"+Flh@TF-7$F^_l$\"+;t\\DUF-7%7$F($\"+;Ft8ZF-7$F/$\"+_DPGZF-7 $F4$\"+#RWrx%F-7%7$F:$\"+E0D)o%F-7$F?$\"+UZ&Qv%F-7$FD$\"+rO(4z%F-7%7$F J$\"+d(Qvj%F-7$FO$\"+6lc/[F-7$FT$\"+q'**f\"[F-7%7$FZ$\"+\\(p#)e%F-7$Fi n$\"+>b$Q&[F-7$F^o$\"+#>Ij$[F-7%7$Fdo$\"+_MnrXF-7$Fio$\"+;=Vq[F-7$F^p$ \"+rg*=%[F-7%7$Fdp$\"+FNHIYF-7$Fip$\"+T<\"=\"[F-7$F^q$\"+c7F>[F-7%7$Fd q$\"+'QtY([F-7$Fiq$\"+#)=VnXF-7$F^r$\"+i-(*oYF-7%7$Fdr$\"+hPa:\\F-7$Fi r$\"+2:cEXF-7$F^s$\"+='Q\"HYF-7%7$Fds$\"+ehK+\\F-7$Fis$\"+5\"z&\\^%F-7$Fiy$\"+UL:F\\F-7$F^z$\"+QBsW[F-7%7$Fdz$\"+ NMCE\\F-7$Fiz$\"+M='e^%F-7$F^[l$\"+%GnIh%F-7%7$Fd[l$\"+%o=T#\\F-7$Fi[l $\"+%e')z^%F-7$F^\\l$\"+A&H^F-7$F/$\"+E?;W^F-7$F4$\"+mQ$H>&F-7%7$F:$\"+++//^F-7$F?$\"+;Uk p^F-7$FD$\"+XJw1_F-7%7$FJ$\"+J#GL0&F-7$FO$\"+&)fN?_F-7$FT$\"+W\"*yJ_F- 7%7$FZ$\"+B#fS+&F-7$Fin$\"+$*\\ip_F-7$F^o$\"+m'>@D&F-7%7$Fdo$\"+EHY() \\F-7$Fio$\"+!H@iG&F-7$F^p$\"+Xbod_F-7%7$Fdp$\"+,I3Y]F-7$Fip$\"+:7gF_F -7$F^q$\"+I21N_F-7%7$Fdq$\"+gGY!H&F-7$Fiq$\"+c8A$)\\F-7$F^r$\"+O(fZ3&F -7%7$Fdr$\"+NKLJ`F-7$Fir$\"+\")4NU\\F-7$F^s$\"+#4G\\/&F-7%7$Fds$\"+Kc6 ;`F-7$Fis$\"+%eov&\\F-7$F^t$\"+ZJ^h]F-7%7$Fdt$\"+feRX\\F-7$Fit$\"+d$)G G`F-7$F^u$\"+c8ll_F-7%7$Fdu$\"+V=?M\\F-7$Fiu$\"+tB[R`F-7$F^v$\"+KyMj_F -7%7$Fdv$\"+F?&eH&F-7$Fiv$\"+*=Ky(\\F-7$F^w$\"+0p;!3&F-7%7$Fdw$\"+E\"R @M&F-7$Fiw$\"+!4X:$\\F-7$F^x$\"+M=jG]F-7%7$Fdx$\"+g%)Gc\\F-7$Fix$\"+cd R<`F-7$F^y$\"+4y(\\E&F-7%7$Fdy$\"++9uI\\F-7$Fiy$\"+;G%HM&F-7$F^z$\"+7= ^g_F-7%7$Fdz$\"+4H.U`F-7$Fiz$\"+38lJ\\F-7$F^[l$\"+en&)G]F-7%7$Fd[l$\"+ e\"3*R`F-7$Fi[l$\"+egxL\\F-7$F^\\l$\"+\"*G%G.&F-7%7$Fd\\l$\"+b)4(H\\F- 7$Fi\\l$\"+hV(RM&F-7$F^]l$\"+M2te_F-7%7$Fd]l$\"+)*4CV`F-7$Fi]l$\"+=KWI \\F-7$F^^l$\"+-,/E]F-7%7$Fd^l$\"+T()[?`F-7$Fi^l$\"+va>`\\F-7$F^_l$\"+k i2d]F-7%7$F($\"+k;JXbF-7$F/$\"++:&*fbF-7$F4$\"+SLs3cF-7%7$F:$\"+u%H)>b F-7$F?$\"+!pLae&F-7$FD$\"+>EbAcF-7%7$FJ$\"+0x6paF-7$FO$\"+fa9OcF-7$FT$ \"+='yvk&F-7%7$FZ$\"+(p[)>aF-7$Fin$\"+nWT&o&F-7$F^o$\"+S\"4zm&F-7%7$Fd o$\"++CD.aF-7$Fio$\"+k2,-dF-7$F^p$\"+>]ZtcF-7%7$Fdp$\"+vC(=Y&F-7$Fip$ \"+*o!RVcF-7$F^q$\"+/-&3l&F-7%7$Fdq$\"+MBD1dF-7$Fiq$\"+I3,*R&F-7$F^r$ \"+5#\\0]&F-7%7$Fdr$\"+4F7ZdF-7$Fir$\"+b/9e`F-7$F^s$\"+mvrgaF-7%7$Fds$ \"+1^!>t&F-7$Fis$\"+e!eLP&F-7$F^t$\"+@EIxaF-7%7$Fdt$\"+L`=h`F-7$Fit$\" +Jy2WdF-7$F^u$\"+I3W\"o&F-7%7$Fdu$\"+<8**\\`F-7$Fiu$\"+Z=FbdF-7$F^v$\" +1t8zcF-7%7$Fdv$\"+,:k6dF-7$Fiv$\"+j;i$R&F-7$F^w$\"+zj&f\\&F-7%7$Fdw$ \"++'Gzv&F-7$Fiw$\"+kXLZ`F-7$F^x$\"+38UWaF-7%7$Fdx$\"+Mz2s`F-7$Fix$\"+ I_=LdF-7$F^y$\"+$Gn2o&F-7%7$Fdy$\"+u3`Y`F-7$Fiy$\"+!HK(edF-7$F^z$\"+'G ,jn&F-7%7$Fdz$\"+$QAyv&F-7$Fiz$\"+#ySuM&F-7$F^[l$\"+KikWaF-7%7$Fd[l$\" +KwpbdF-7$Fi[l$\"+Kbc\\`F-7$F^\\l$\"+lBj[aF-7%7$Fd\\l$\"+H$*\\X`F-7$Fi \\l$\"+NQwfdF-7$F^]l$\"+3-_ucF-7%7$Fd]l$\"+s/.fdF-7$Fi]l$\"+#pKiM&F-7$ F^^l$\"+w&H=W&F-7%7$Fd^l$\"+:#yit&F-7$Fi^l$\"+\\\\)*o`F-7$F^_l$\"+Qd'G Z&F-7%7$F($\"+Q65hfF-7$F/$\"+u4uvfF-7$F4$\"+9G^CgF-7%7$F:$\"+[*=c$fF-7 $F?$\"+kJA,gF-7$FD$\"+$4U$QgF-7%7$FJ$\"+zr!\\)eF-7$FO$\"+L\\$>0'F-7$FT $\"+#4oL1'F-7%7$FZ$\"+r\"Qc$eF-7$Fin$\"+TR?,hF-7$F^o$\"+9')p$3'F-7%7$F do$\"+u=/>eF-7$Fio$\"+Q-!y6'F-7$F^p$\"+$\\k#*3'F-7%7$Fdp$\"+\\>mxeF-7$ Fip$\"+j,=fgF-7$F^q$\"+y'Rm1'F-7%7$Fdq$\"+3=/AhF-7$Fiq$\"+/.![\"eF-7$F ^r$\"+%oQj\"fF-7%7$Fdr$\"+$=7H;'F-7$Fir$\"+H*HRx&F-7$F^s$\"+Sq]weF-7%7 $Fds$\"+!e%pZhF-7$Fis$\"+Kv9*y&F-7$F^t$\"+&4#4$*eF-7%7$Fdt$\"+2[(px&F- 7$Fit$\"+0t')fhF-7$F^u$\"+/.B(4'F-7%7$Fdu$\"+\"z!yldF-7$Fiu$\"+@81rhF- 7$F^v$\"+!yE\\4'F-7%7$Fdv$\"+v4VFhF-7$Fiv$\"+P6T4eF-7$F^w$\"+`eu6fF-7% 7$Fdw$\"+u!=P<'F-7$Fiw$\"+QS7jdF-7$F^x$\"+#y5-'eF-7%7$Fdx$\"+3u'yy&F-7 $Fix$\"+/Z(*[hF-7$F^y$\"+dnb'4'F-7%7$Fdy$\"+[.KidF-7$Fiy$\"+k<_uhF-7$F ^z$\"+g24#4'F-7%7$Fdz$\"+d=hthF-7$Fiz$\"+c-BjdF-7$F^[l$\"+1dVgeF-7%7$F d[l$\"+1r[rhF-7$Fi[l$\"+1]NldF-7$F^\\l$\"+R=UkeF-7%7$Fd\\l$\"+.))GhdF- 7$Fi\\l$\"+4LbvhF-7$F^]l$\"+#o4.4'F-7%7$Fd]l$\"+Y*>[<'F-7$Fi]l$\"+m@-i dF-7$F^^l$\"+]!>w&eF-7%7$Fd^l$\"+*on?:'F-7$Fi^l$\"+BWx%y&F-7$F^_l$\"+7 _l))eF-7%7$F($\"+71*oP'F-7$F/$\"+[/`\"R'F-7$F4$\"+)G-.W'F-7%7$F:$\"+A% 39N'F-7$F?$\"+QE,(*='F-7$F^s$\"+9lH#H'F- 7%7$Fds$\"+aS[jlF-7$Fis$\"+1q$\\?'F-7$F^t$\"+p:))3jF-7%7$Fdt$\"+\"GkF> 'F-7$Fit$\"+znlvlF-7$F^u$\"+y(>I^'F-7%7$Fdu$\"+l-d\"='F-7$Fiu$\"+&z]oe 'F-7$F^v$\"+air5lF-7%7$Fdv$\"+\\/AVlF-7$Fiv$\"+61?DiF-7$F^w$\"+F``FjF- 7%7$Fdw$\"+[v]*e'F-7$Fiw$\"+7N\"*yhF-7$F^x$\"+c-+wiF-7%7$Fdx$\"+#)ol.i F-7$Fix$\"+yTwklF-7$F^y$\"+JiM7lF-7%7$Fdy$\"+A)4\"yhF-7$Fiy$\"+Q7J!f'F -7$F^z$\"+M-)y]'F-7%7$Fdz$\"+J8S*e'F-7$Fiz$\"+I(>!zhF-7$F^[l$\"+!=DiF' F-7%7$Fd[l$\"+!ewse'F-7$Fi[l$\"+![W6='F-7$F^\\l$\"+88@!G'F-7%7$Fd\\l$ \"+x#yq<'F-7$Fi\\l$\"+$yU8f'F-7$F^]l$\"+c\"*41lF-7%7$Fd]l$\"+?%41f'F-7 $Fi]l$\"+S;\"y<'F-7$F^^l$\"+C&3MF'F-7%7$Fd^l$\"+jr&yc'F-7$Fi^l$\"+(*Qc +iF-7$F^_l$\"+'oWWI'F-7%7$F($\"+'3!o#z'F-7$F/$\"+A*>t!oF-7$F4$\"+i<4co F-7%7$F:$\"+'*y>nnF-7$F?$\"+7@!G$oF-7$FD$\"+T5#*poF-7%7$FJ$\"+Fh[;nF-7 $FO$\"+\")Q^$)oF-7$FT$\"+Sq%\\*oF-7%7$FZ$\"+>r@nmF-7$Fin$\"+*)GyKpF-7$ F^o$\"+ivF:pF-7%7$Fdo$\"+A3i]mF-7$Fio$\"+'=z$\\pF-7$F^p$\"+TM%3#pF-7%7 $Fdp$\"+(*3C4nF-7$Fip$\"+6\"f2*oF-7$F^q$\"+E'=#)*oF-7%7$Fdq$\"+c2i`pF- 7$Fiq$\"+_#zjk'F-7$F^r$\"+Kw\"zu'F-7%7$Fdr$\"+J6\\%*pF-7$Fir$\"+x)3bg' F-7$F^s$\"+))f33nF-7%7$Fds$\"+GNFzpF-7$Fis$\"+![E2i'F-7$F^t$\"+V5nCnF- 7%7$Fdt$\"+bPb3mF-7$Fit$\"+`iW\"*pF-7$F^u$\"+_#4)GpF-7%7$Fdu$\"+R(ftf' F-7$Fiu$\"+p-k-qF-7$F^v$\"+Gd]EpF-7%7$Fdv$\"+B*4!fpF-7$Fiv$\"+&3!*4k'F -7$F^w$\"+,[KVnF-7%7$Fdw$\"+AqH0qF-7$Fiw$\"+')Hq%f'F-7$F^x$\"+I(*y\"p' F-7%7$Fdx$\"+cjW>mF-7$Fix$\"+_Ob!)pF-7$F^y$\"+0d8GpF-7%7$Fdy$\"+'H**Qf 'F-7$Fiy$\"+7251qF-7$F^z$\"+3(pO#pF-7%7$Fdz$\"+03>0qF-7$Fiz$\"+/#4[f'F -7$F^[l$\"+aY,#p'F-7%7$Fd[l$\"+ag1.qF-7$Fi[l$\"+aR$pf'F-7$F^\\l$\"+(y+ gp'F-7%7$Fd\\l$\"+^x'Gf'F-7$Fi\\l$\"+dA82qF-7$F^]l$\"+I'))=#pF-7%7$Fd] l$\"+%*))R1qF-7$Fi]l$\"+96g$f'F-7$F^^l$\"+)*z>*o'F-7%7$Fd^l$\"+Pmk$)pF -7$Fi^l$\"+rLN;mF-7$F^_l$\"+gTB?nF--%&COLORG6&%$RGBG$\"\"(!\"\"$\"#&)! \"#$\"#vFd][l-%+AXESLABELSG6$%\"xG%%y(x)G-%%VIEWG6$;$\"++++]FF*$\"++++ D_F-;$!++++&\\\"F-$\"++++&>(F-" 2 637 362 362 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "soln_ curve1 := plot(rhs(soln),x= 1/2..5,color=magenta, thickness=2):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "display(\{direction_field_pl ot,soln_curve1\});" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6%7]s7$$ \"1+++++++]!#;$\"1)QBd%*=xd#F*7$$\"1++]P>(3)fF*$\"1)yDebD(zJF*7$$\"1+] ilLKMoF*$\"1%QMp/%=$y$F*7$$\"1++Dc(=Tz(F*$\"1g=%=S#H%f%F*7$$\"1++v$Hw- w)F*$\"13))f1a)yg&F*7$$\"1**\\7`=%=s*F*$\"18*\\]'=:voF*7$$\"1+Dc@OLh5! #:$\"1bC1]-2K$)F*7$$\"1+D1*pUO:\"FI$\"1`.ahSe;5FI7$$\"1+D1z)3\"\\7FI$ \"1[xu/m`U7FI7$$\"1+D\"y*)oUM\"FI$\"1r(\\)Qef,:FI7$$\"1++vtE:U9FI$\"1: 3[>Nz\"FI7$$\"1+](ovo$G:FI$\"1g%*Rczld?FI7$$\"1++DYwUD;FI$\"1VZ!ej:) QBFI7$$\"1++vo])Gs\"FI$\"1,vxF,VrDFI7$$\"1++D6U%)pz%*ys9t#FI7$$ \"1]i!RvY%f=FI$\"1Gs+c/:VFFI7$$\"1vV)RXo2)=FI$\"1dHx9t[[FFI7$$\"1+D1a, 4->FI$\"136B\"zdsu#FI7$$\"1vVtFI$\"17GFO[+PFFI7$$\"1]iS\"G(z_>FI$ \"1WcuE@,FI$\"1+]zZK>(o#FI7$$\"1++v3W].?FI$\"1C+%H x#fZEFI7$$\"1+](o**fk/#FI$\"1z>\"GQw(eDFI7$$\"1+++&e:%*3#FI$\"1'=NX2MW W#FI7$$\"1+Dc12N*=#FI$\"1![f3YB45#FI7$$\"1++]A-\"yF#FI$\"1#)Gnk^IRJo\"FI7$$\"1]P%[D@+q#FI$\"1T*4-p'\\y>FI7$$\"1+](o%)yxu#FI$\"15J> BB#pL#FI7$$\"1](oHc&Q(z#FI$\"1%fHv_mtv#FI7$$\"1+D1zA*p%GFI$\"1?0[r&y5? $FI7$$\"1++Dr]'4v$)=e$FI7$$\"1+vVjyNLHFI$\"1rP-#*RvLRFI7$$ \"1]7.ik**zHFI$\"1mj!Qe)faUFI7$$\"1+]ig]jEIFI$\"1Z!*=%3?u[%FI7$$\"1]Pf yhs]IFI$\"1[DZI$4bc%FI7$$\"1+Dc'H<[2$FI$\"1+GVdoa6YFI7$$\"1voabG'o3$FI $\"1a;bWQ'>i%FI7$$\"1]7`9%3*)4$FI$\"1QC(Q\"evBYFI7$$\"1Dc^tR&46$FI$\"1 JXr\"p8oh%FI7$$\"1++]K&**H7$FI$\"1b8@b#y5g%FI7$$\"1+DJ]k8qJFI$\"1.!=uB !ebWFI7$$\"1+]7oLFdSS#FI7$$\"1+vo>#o_X$FI$\"1383lTuc?FI7$$\"1 ++]A)p2]$FI$\"1XIWzUMM=FI7$$\"1]7y!\\:H^$FI$\"1h=`fI/,=FI7$$\"1+D1f61D NFI$\"1k7p2E&)zwS#=FI7$$\"1++vo^$zf$FI$\"1-.lB gZE>FI7$$\"1]iS\"He>k$FI$\"1mka@gDYAFI7$$\"1+D199)fo$FI$\"1^%eEhh:s#FI 7$$\"1v$4Y'e/5PFI$\"1Zs[!yFX.$FI7$$\"1]i::.6MPFI$\"1.41Ue#\\P$FI7$$\"1 DJqlZ$[nRFI$\"1OYV\"QZ,&fFI7$$\"1(oz\"*>`!zRFI$\"1 \"z\\NP\"3`fFI7$$\"1voa0Ki!*RFI$\"1oT'p&G4RfFI7$$\"1iS\">@$>-SFI$\"1w' *e&\\c\"3fFI7$$\"1]7G=Kw8SFI$\"1]*)3UhRgeFI7$$\"1Dc,JK!p.%FI$\"1Q(3(\\ *fcr&FI7$$\"1++vVK/gSFI$\"1(fD#p%H*3bFI7$$\"1C\"yDpoU3%FI$\"1&erP>UJB& FI7$$\"1]iSTT\\3TFI$\"1#*H)>JIm!\\FI7$$\"1vVB!f>F8%FI$\"1/.=.K+UXFI7$$ \"1*\\i!R]%p:%FI$\"1E<,0x'R:%FI7$$\"1voaDqF!=%FI$\"1zJLfrJtPFI7$$\"1^7 .7!4O?%FI$\"1OTB;zZ,MFI7$$\"1Fc^)*4%pA%FI$\"1(o1mCFT0$FI7$$\"1,++&)HF] UFI$\"1,Pqo!zlu#FI7$$\"1^P46L8uUFI$\"1E7@g#G\")[#FI7$$\"1,v=PO*zH%FI$ \"1e.h,5w*H#FI7$$\"1wVB+Q#*4VFI$\"1p:_$z:aB#FI7$$\"1]7GjR&=K%FI$\"1uN& eG$\\#>#FI7$$\"1C\"Gj7%yLVFI$\"1%*f3A5)=<#FI7$$\"1+]P*G9dM%FI$\"1*ej%Q )RU<#FI7$$\"1](o/zRIR%FI$\"1F&)\\IoY9CFI7$$\"1+Dc\"Hl.W%FI$\"1[t%fsNT+ $FI7$$\"1voz,*3@Y%FI$\"1:n!)GF3tLFI7$$\"1]7.7D&Q[%FI$\"1rXtgRP)y$FI7$$ \"1DcEAhf0XFI$\"1%R@:[2gB%FI7$$\"1++]K(Rt_%FI$\"1J+&*)4N-q%FI7$$\"1\\P fj.E_XFI$\"13d`-'>3B&FI7$$\"1+vo%*4=xXFI$\"1HUg_5gMdFI7$$\"1]7yD;5-YFI $\"1I_$oqac='FI7$$\"1+](oDAqi%FI$\"1;xnA`))flFI7$$\"1]iSm:J\\YFI$\"1BQ ,h%yB\"oFI7$$\"1+v$f(3grYFI$\"1_)e()=\"zupFI7$$\"17.K.KqFI7$$\"1Qf3eyJ)o%FI$\"1MW$GYRB.(FI 7$$\"1](oa=!*Qp%FI$\"1$oA()y=)QqFI7$$\"1j:&G^i%*p%FI$\"1Ou(y]k)QqFI7$$ \"1wVBS[.0ZFI$\"1#R'ovOXKqFI7$$\"1)=qFI7$$\"1++ +&\\zhr%FI$\"122.^*f-+(FI7$$\"1D1*yaW*RZFI$\"1ZD$fMRl%oFI7$$\"1]7y+'4P w%FI$\"1gPfgvr#e'FI7$$\"1v=n`YZ(y%FI$\"1S\")p64!4A'FI7$$\"1+Dc1(R7\"[F I$\"1'eqPbx(ydFI7$$\"1\\7`%*e)R$[FI$\"1]wZDD>,`FI7$$\"1++]#3Kn&[FI$\"1 @bo-0%Qz%FI7$$\"1](o/Fy%z[FI$\"1\"[w997@G%FI7$$\"1+vVeWA-\\FI$\"1gd)R( eX#z$FI7$$\"1C\"GQMom#\\FI$\"1=xIDrw?LFI7$$\"1](=#HA6^\\FI$\"1@JyJ>?NH FI7$$\"1v$4Y6cb(\\FI$\"1aebAY5iEFI7$$\"\"&\"\"!$\"1;8MqH*>_#FI-%'COLOU RG6&%$RGBG$\"*++++\"!\")FfcmF]dm-%*THICKNESSG6#\"\"#-F$6]dl7%7$$\"+\\P _;Q!#5$!+=*>t5\"!\"*7$$\"+^iZ$='Fjdm$!+#3!o#4\"F]em7$$\"+p?fgcFjdm$!+U #3R/\"F]em7%7$$\"+RS/*>'Fjdm$!+3@!G8\"F]em7$$\"+n!)zP&)Fjdm$!+#*y>n5F] em7$$\"+/6t%)zFjdm$!+j*y+.\"F]em7%7$$\"+pCQ_')Fjdm$!+xQ^$=\"F]em7$$\"+ u,8#3\"F]em$!+Bh[;5F]em7$$\"+&*)yK-\"F]em$!+kH005F]em7%7$$\"+)y1%>6F]e m$!+&)GyK7F]em7$$\"+Wek,8F]em$!+]6\"F]em7$$\"+V3v!z\"F]e m$!+$*3C45F]em7$$\"+wHpJ%3+#F]em$!+_2i`7F]em7$$\"+J&o\"))>F]em$!+sB3_6F]em7%7$$\"+l= 1;@F]em$!+M()3b!*Fjdm7$$\"+2ws*>#F]em$!+F6\\%H\"F]em7$$\"+k*4$4AF]em$! +;S\">>\"F]em7%7$$\"+*RuZL#F]em$!+gZE2#*Fjdm7$$\"+$G*paCF]em$!+CNFz7F] em7$$\"+TUEaCF]em$!+h*G`<\"F]em7%7$$\"+ZJT&e#F]em$!+\\iW\"H\"F]em7$$\" +XZuxEF]em$!+9v`&3*Fjdm7$$\"+_9\\IEF]em$!+Bv!>r*Fjdm7%7$$\"+)*\\'>%GF] em$!+l-k-8F]em7$$\"+/r([*GF]em$!+_tft*)Fjdm7$$\"+(HkX&GF]em$!+gF%\\t*F jdm7%7$$\"+?k(*GIF]em$!+33!*4%*Fjdm7$$\"+#*)\\:=$F]em$!+>*4!f7F]em7$$ \"+%eg6<$F]em$!+._nc6F]em7%7$$\"+*HVMK$F]em$!+?)Hq%*)Fjdm7$$\"+BswgLF] em$!+=qH08F]em7$$\"+\"p@>Q$F]em$!+u-@37F]em7%7$$\"+3WC?NF]em$!+[Ob!G\" F]em7$$\"+C.lPOF]em$!+BNY%>*Fjdm7$$\"+W%>le$F]em$!+!*Hk=(*Fjdm7%7$$\"+ xcE+QF]em$!+32518F]em7$$\"+lKJJQF]em$!+;H**Q*)Fjdm7$$\"+\"[T_z$F]em$!+ bHIj(*Fjdm7%7$$\"+]VfLSF]em$!+&*>4[*)Fjdm7$$\"+-)o;2%F]em$!+,3>08F]em7 $$\"+]ck#4%F]em$!+^`)z?\"F]em7%7$$\"+G!*4kUF]em$!+'\\R$p*)Fjdm7$$\"+M$ [[J%F]em$!+]g1.8F]em7$$\"+@%yFL%F]em$!+<#**R?\"F]em7%7$$\"+nF=;XF]em$! +`A828F]em7$$\"+0)[k`%F]em$!+ounG*)Fjdm7$$\"+(RkD]%F]em$!+SP6\"y*Fjdm7 %7$$\"+nw(*[ZF]em$!++6,O*)Fjdm7$$\"+:\"Qtx%F]em$!+!*))R18F]em7$$\"+X,f +[F]em$!+1?!3@\"F]em7%7$$\"+?u\\W\\F]em$!+rO`j\"*Fjdm7$$\"+sD]b]F]em$! +Lmk$G\"F]em7$$\"+i9id]F]em$!+Wewz6F]em7%7$Fhdm$!+TWI:pFjdm7$F_em$!+&3 1*onFjdm7$Fdem$!+#o(=\"G'Fjdm7%7$Fjem$!+Rj7qrFjdm7$F_fm$!+(=%39lFjdm7$ Fdfm$!+,\\*G9'Fjdm7%7$Fjfm$!+OSCxwFjdm7$F_gm$!+!\\mp+'Fjdm7$Fdgm$!+,\\ j#*eFjdm7%7$Fjgm$!+8T$*p\")Fjdm7$F_hm$!+8kF9bFjdm7$Fdhm$!+)oH$*o&Fjdm7 %7$Fjhm$!+%3(*eL)Fjdm7$F_im$!+UMJ[`Fjdm7$Fdim$!+()3nLcFjdm7%7$Fjim$!+O jp\\xFjdm7$F_jm$!+!>9X$fFjdm7$Fdjm$!+R!>*feFjdm7%7$Fjjm$!+Xx*eI&Fjdm7$ F_[n$!+\"y7$y$)Fjdm7$Fd[n$!+z*GHO(Fjdm7%7$Fj[n$!+(*R>(*[Fjdm7$F_\\n$!+ Hl,(y)Fjdm7$Fd\\n$!+AaChxFjdm7%7$Fj\\n$!+B+P\\]Fjdm7$F_]n$!+.0%[j)Fjdm 7$Fd]n$!+w[R&f(Fjdm7%7$Fj]n$!+\\xcc()Fjdm7$F_^n$!+xFkF\\Fjdm7$Fd^n$!+' y7Sb&Fjdm7%7$Fj^n$!+6z]o))Fjdm7$F__n$!+:Eq:[Fjdm7$Fd_n$!+B![qd&Fjdm7%7 $Fj_n$!+rg+__Fjdm7$F_`n$!+bW?K%)Fjdm7$Fd`n$!+*Hd)3uFjdm7%7$Fj`n$!+$3N \"*y%Fjdm7$F_an$!+Va2&*))Fjdm7$Fdan$!+**z?CzFjdm7%7$Fjan$!+S!z%Fjdm7$F_dn$!+oK,%*))Fjdm 7$Fddn$!+r(e>#zFjdm7%7$Fjdn$!+fZW6[Fjdm7$F_en$!+ndws))Fjdm7$Fden$!+Tu4 #)yFjdm7%7$Fjen$!+&zFM\"*)Fjdm7$F_fn$!+JFyqZFjdm7$Fdfn$!+.!>Ki&Fjdm7%7 $Fjfn$!+jj6yZFjdm7$F_gn$!+jT41*)Fjdm7$Fdgn$!+C`7]zFjdm7%7$Fjgn$!+M*Qc+ &Fjdm7$F_hn$!+#fr&y')Fjdm7$Fdhn$!+/PwRwFjdm7%7$Fhdm$!+/(4uv#Fjdm7$F_em $!+[8,6EFjdm7$Fdem$!+XHHB@Fjdm7%7$Fjem$!+-;B7IFjdm7$F_fm$!+]%*=cBFjdm7 $Fdfm$!+k,+&)>Fjdm7%7$Fjfm$!+*H\\$>NFjdm7$F_gm$!+`<2\\=Fjdm7$Fdgm$!+k, uM\"Fjdm7$Fdim$!+]hxv9Fjdm7%7$Fjim$!+*f,=f$ Fjdm7$F_jm$!+`%>mx\"Fjdm7$Fdjm$!+-V--9Fjdm7%7$Fj_n$!+ M86%4\"Fjdm7$F_`n$!+=(4VF%Fjdm7$Fd`n$!+iD'4D$Fjdm7%7$Fj`n$!*Y.CJ'Fjdm7 $F_an$!+12=PZFjdm7$Fdan$!+iKJmPFjdm7%7$Fjan$!+.qu*[%Fjdm7$F_bn$!*\\Sny )Fjdm7$Fdbn$!+;N&GS\"Fjdm7%7$Fjbn$!+5w@XZFjdm7$F_cn$!*UM?B'Fjdm7$Fdcn$ !+\"[8vW\"Fjdm7%7$Fjcn$!*@DIK'Fjdm7$F_dn$!+J&=ht%Fjdm7$Fddn$!+MS1kPFjd m7%7$Fjdn$!*A+b`'Fjdm7$F_en$!+I5([r%Fjdm7$Fden$!+/F?CPFjdm7%7$Fjen$!+e I`bZFjdm7$F_fn$!*%*z)GhFjdm7$Fdfn$!+mUKl9Fjdm7%7$Fjfn$!*E;A?'Fjdm7$F_g n$!+E%*>[ZFjdm7$Fdgn$!+(eIAz$Fjdm7%7$Fjgn$!*(>Wx%)Fjdm7$F_hn$!+bon?XFj dm7$Fdhn$!+n*o=[$Fjdm7%7$Fhdm$\"+L][+9Fjdm7$F_em$\"+*Q$)oa\"Fjdm7$Fdem $\"+#z,Y.#Fjdm7%7$Fjem$\"+NJmX6Fjdm7$F_fm$\"+(G0kE$Fjdm7$F_]n$!*H50>$Fjdm7$Fd]n$\"*)f% R?(Fjdm7%7$Fj]n$!*v#y2WFjdm7$F_^n$\"+(pY\")Q$Fjdm7$Fd^n$\"+)ow'Fjdm7%7$Fjem$\"+syb.`Fjdm7$F_fm$\"+C+gffFjd m7$Fdfm$\"+5$*yIjFjdm7%7$Fjfm$\"+v,W'z%Fjdm7$F_gm$\"+@xrmkFjdm7$Fdgm$ \"+5$\\5e'Fjdm7%7$Fjgm$\"+)4]PI%Fjdm7$F_hm$\"+)z2%fpFjdm7$Fdhm$\"+CXN% y'Fjdm7%7$Fjhm$\"+FryPTFjdm7$F_im$\"+p2PDrFjdm7$Fdim$\"+CL,SoFjdm7%7$F jim$\"+vy)Rs%Fjdm7$F_jm$\"+@+pFjdm7%7$Fj^n$\"++j<0OFjdm7$F__n$\"+'f\")zl(Fjdm7$Fd_ n$\"+)=Om*oFjdm7%7$Fj_n$\"+S\"y;A(Fjdm7$F_`n$\"+c(z9/%Fjdm7$Fd`n$\"+7p #[1&Fjdm7%7$Fj`n$\"+G\"\\Xo(Fjdm7$F_an$\"+o(3'yNFjdm7$Fdan$\"+7iZ\\XFj dm7%7$Fjan$\"+rC/EQFjdm7$F_bn$\"+Da6PuFjdm7$Fdbn$\"+ef$H\"pFjdm7%7$Fjb n$\"+k=dqNFjdm7$F_cn$\"+Kge#p(Fjdm7$Fdcn$\"+$*fFooFjdm7%7$Fjcn$\"+`p[$ o(Fjdm7$F_dn$\"+V4nzNFjdm7$Fddn$\"+Sas^XFjdm7%7$Fjdn$\"+_%RAm(Fjdm7$F_ en$\"+W%=4g$Fjdm7$Fden$\"+qne\"f%Fjdm7%7$Fjen$\"+;kDgNFjdm7$F_fn$\"+![ ,Hq(Fjdm7$Fdfn$\"+4_Y]oFjdm7%7$Fjfn$\"+[yc&p(Fjdm7$F_gn$\"+[+fnNFjdm7$ Fdgn$\"+())eN_%Fjdm7%7$Fjgn$\"+x_/ouFjdm7$F_hn$\"+>E6&z$Fjdm7$Fdhn$\"+ 20#R$[Fjdm7%7$Fhdm$\"+2XF;(*Fjdm7$F_em$\"+jGni)*Fjdm7$Fdem$\"+F\"R].\" F]em7%7$Fjem$\"+4EXh%*Fjdm7$F_fm$\"+w%\\<,\"F]em7$Fdfm$\"+0%o)[5F]em7% 7$Fjfm$\"+7\\La*)Fjdm7$F_gm$\"+Y7Yi5F]em7$Fdgm$\"+0W*Q2\"F]em7%7$Fjgm$ \"+N[kh%)Fjdm7$F_hm$\"+a-t66F]em7$Fdhm$\"+F\\A%4\"F]em7%7$Fjhm$\"+k=o& H)Fjdm7$F_im$\"+^lKG6F]em7$Fdim$\"+13z*4\"F]em7%7$Fjim$\"+7E)=)))Fjdm7 $F_jm$\"+wkqp5F]em7$Fdjm$\"+\"*f;x5F]em7%7$Fjjm$\"+?\"oD8\"F]em7$F_[n$ \"+nhE`#)Fjdm7$Fd[n$\"+p*\\'o#*Fjdm7%7$Fj[n$\"+&\\QM<\"F]em7$F_\\n$\"+ >CcWyFjdm7$Fd\\n$\"+ENLq))Fjdm7%7$Fj\\n$\"+$*3Ae6F]em7$F_]n$\"+X%Qn*zF jdm7$Fd]n$\"+sS=O!*Fjdm7%7$Fj]n$\"+*>6](yFjdm7$F_^n$\"+)Fjdm7$Fd`n$\"+\\;sA#*F jdm7%7$Fj`n$\"+(QWU=\"F]em7$F_an$\"+0N]OxFjdm7$Fdan$\"+\\4P2()Fjdm7%7$ Fjan$\"+3s$R)zFjdm7$F_bn$\"+;5]f6F]em7$Fdbn$\"+pI326F]em7%7$Fjbn$\"+,m YGxFjdm7$F_cn$\"+x![]=\"F]em7$Fdcn$\"+tqh-6F]em7%7$Fjcn$\"+p\"QT=\"F]e m7$F_dn$\"+!olvt(Fjdm7$Fddn$\"+x,i4()Fjdm7%7$Fjdn$\"+>M,#=\"F]em7$F_en $\"+\"=8)exFjdm7$Fden$\"+2:[\\()Fjdm7%7$Fjen$\"+`6:=xFjdm7$F_fn$\"+A'z g=\"F]em7$Fdfn$\"+&*f$35\"F]em7%7$Fjfn$\"+fiM&=\"F]em7$F_gn$\"+&y%[DxF jdm7$Fdgn$\"+COX\"o)Fjdm7%7$Fjgn$\"+,Sfi6F]em7$F_hn$\"+ct+`zFjdm7$Fdhn $\"+W_\"=**)Fjdm7%7$Fhdm$\"+CpT(Q\"F]em7$F_em$\"+gn0-9F]em7$Fdem$\"++' G3X\"F]em7%7$Fjem$\"+MZ$>O\"F]em7$F_fm$\"+]*QvU\"F]em7$Fdfm$\"+zylk9F] em7%7$Fjfm$\"+lHA68F]em7$F_gm$\"+>2Dy9F]em7$Fdgm$\"+yQo*[\"F]em7%7$Fjg m$\"+dR&>E\"F]em7$F_hm$\"+F(>v_\"F]em7$Fdhm$\"++W,5:F]em7%7$Fjhm$\"+gw NX7F]em7$F_im$\"+Cg6W:F]em7$Fdim$\"+z-e::F]em7%7$Fjim$\"+Nx(RI\"F]em7$ F_jm$\"+\\f\\&[\"F]em7$Fdjm$\"+ka&H\\\"F]em7%7$Fjjm$\"+%fd$[:F]em7$F_[ n$\"+!4;6C\"F]em7$Fd[n$\"+qWlU8F]em7%7$Fj[n$\"+pzA*e\"F]em7$F_\\n$\"+: dC+7F]em7$Fd\\n$\"+EG#GI\"F]em7%7$Fj\\n$\"+m.,u:F]em7$F_]n$\"+=LY:7F]e m7$Fd]n$\"+\")yS>8F]em7%7$Fj]n$\"+$f!H.7F]em7$F_^n$\"+\"4$='e\"F]em7$F d^n$\"+!4YN_\"F]em7%7$Fj^n$\"+xl4#>\"F]em7$F__n$\"+2rP(f\"F]em7$Fd_n$ \"+mDC@:F]em7%7$Fj_n$\"+hnu`:F]em7$F_`n$\"+BpsN7F]em7$Fd`n$\"+R;1Q8F]e m7%7$Fj`n$\"+gQ.+;F]em7$F_an$\"+C)R%*=\"F]em7$Fdan$\"+ol_'G\"F]em7%7$F jan$\"+%>$=97F]em7$F_bn$\"+!\\!Hv:F]em7$Fdbn$\"+VD(G_\"F]em7%7$Fjbn$\" +Mhj)=\"F]em7$F_cn$\"+]v$3g\"F]em7$Fdcn$\"+YlS=:F]em7%7$Fjcn$\"+Vw#**f \"F]em7$F_dn$\"+Uga*=\"F]em7$Fddn$\"+#\\^nG\"F]em7%7$Fjdn$\"+#*G!yf\"F ]em7$F_en$\"+#zq;>\"F]em7$Fden$\"+Dwt!H\"F]em7%7$Fjen$\"+*e/w=\"F]em7$ F_fn$\"+&4p=g\"F]em7$Fdfn$\"+oai;:F]em7%7$Fjfn$\"+Kd8,;F]em7$F_gn$\"+_ zL)=\"F]em7$Fdgn$\"+O[$RG\"F]em7%7$Fjgn$\"+vMQy:F]em7$F_hn$\"+4-467F]e m7$Fdhn$\"+)*4(\\J\"F]em7%7$Fhdm$\"+)R1K!=F]em7$F_em$\"+Mi%y\"=F]em7$F dem$\"+u!=m'=F]em7%7$Fjem$\"+3UsxSS*=F]em7$Fdgm$\"+_LZ0>F]em7% 7$Fjgm$\"+JMux;F]em7$F_hm$\"+,#4L%>F]em7$Fdhm$\"+uQ!e#>F]em7%7$Fjhm$\" +Mr9h;F]em7$F_im$\"+)\\0*f>F]em7$Fdim$\"+`(p8$>F]em7%7$Fjim$\"+4sw>F]em7$Fdjm$\"+Q\\u3>F]em7%7$Fjjm$\"+oq9k>F]em7$F_[n$ \"+kb!pl\"F]em7$Fd[n$\"+WRWeF]em7$F_]n$\"+#z_7j\"F]e m7$Fd]n$\"+bt>N;F]em7$F_^n$\"+lD(>+#F]em7$Fd^n$\" +kbLR>F]em7%7$Fj^n$\"+^g)yg\"F]em7$F__n$\"+\"emJ,#F]em7$Fd_n$\"+S?.P>F ]em7%7$Fj_n$\"+Ni`p>F]em7$F_`n$\"+(R;:l\"F]em7$Fd`n$\"+86&Qv\"F]em7%7$ Fj`n$\"+ML#e,#F]em7$F_an$\"+)HH_g\"F]em7$Fdan$\"+UgJ-F]em7$Fdbn$\"+F]em7%7$Fjbn$\"+3cU/;F]em 7$F_cn$\"+Cqi;?F]em7$Fdcn$\"+?g>M>F]em7%7$Fjcn$\"+F]em7%7$Fjfn$\"+1_#p,#F]em7$F_gn$\"+Eu7/;F]em7$Fdgn$\"+5Vs*p\"F]e m7%7$Fjgn$\"+\\H<%*>F]em7$F_hn$\"+$ozoi\"F]em7$Fdhn$\"+s/wI#F]em7$F_fm$\"+)*y6fAF]em7$Fdfm$\"+FoB'H#F]em7%7$Fjfm$\"+8>!G9#F]em7 $F_gm$\"+n'H)4BF]em7$Fdgm$\"+EGE@BF]em7%7$Fjgm$\"+0H`$4#F]em7$F_hm$\"+ v')4fBF]em7$Fdhm$\"+[LfTBF]em7%7$Fjhm$\"+3m$p2#F]em7$F_im$\"+s\\pvBF]e m7$Fdim$\"+F#frM#F]em7%7$Fjim$\"+$ocb8#F]em7$F_jm$\"+(*[2?F]em7$F_fn$\"+V![MV#F]em7$Fdfn$\"+;W?[BF]em7%7$Fjfn$\"+!o9FV# F]em7$F_gn$\"++p\"*>?F]em7$Fdgn$\"+%y8b6#F]em7%7$Fjgn$\"+BC'*4CF]em7$F _hn$\"+d\"pE/#F]em7$Fdhn$\"+Y*\\l9#F]em7%7$Fhdm$\"+Y`yMEF]em7$F_em$\"+ #=D%\\EF]em7$Fdem$\"+Aq>)p#F]em7%7$Fjem$\"+cJI4EF]em7$F_fm$\"+st!\\n#F ]em7$Fdfm$\"+,j-7FF]em7%7$Fjfm$\"+(Q\"feDF]em7$F_gm$\"+T\">cs#F]em7$Fd gm$\"++B0PFF]em7%7$Fjgm$\"+zBK4DF]em7$F_hm$\"+\\\"))[x#F]em7$Fdhm$\"+A GQdFF]em7%7$Fjhm$\"+#3EF\\#F]em7$F_im$\"+YW[\"z#F]em7$Fdim$\"+,([Hw#F] em7%7$Fjim$\"+dhM^DF]em7$F_jm$\"+rV'Gt#F]em7$Fdjm$\"+')QKSFF]em7%7$Fjj m$\"+;gs&z#F]em7$F_[n$\"+7X[)[#F]em7$Fd[n$\"+#*G-!f#F]em7%7$Fj[n$\"+\" R'fOGF]em7$F_\\n$\"+PThZCF]em7$Fd\\n$\"+[7>]DF]em7%7$Fj\\n$\"+)yy8#GF] em7$F_]n$\"+S<$GY#F]em7$Fd]n$\"+.jxmDF]em7%7$Fj]n$\"+:!f1X#F]em7$F_^n$ \"+8:bLGF]em7$Fd^n$\"+7X\"4x#F]em7%7$Fj^n$\"+**\\YRCF]em7$F__n$\"+HbuW GF]em7$Fd_n$\"+))4hoFF]em7%7$Fj_n$\"+$=:6!GF]em7$F_`n$\"+X`4$[#F]em7$F d`n$\"+h+V&e#F]em7%7$Fj`n$\"+#G-u%GF]em7$F_an$\"+Y#3oV#F]em7$Fdan$\"+! *\\*Q`#F]em7%7$Fjan$\"+;;bhCF]em7$F_bn$\"+7*eE#GF]em7$Fdbn$\"+l4CqFF]e m7%7$Fjbn$\"+cX+OCF]em7$F_cn$\"+sf?[GF]em7$Fdcn$\"+o\\xlFF]em7%7$Fjcn$ \"+lgHZGF]em7$F_dn$\"+kW\"pV#F]em7$Fddn$\"+9*>T`#F]em7%7$Fjdn$\"+98$F]em7$Fdhm$\"+'HsJ<$F]em7%7$Fjhm$\"+cb^ 3HF]em7$F_im$\"+?RF2KF]em7$Fdim$\"+v\"Q(yJF]em7%7$Fjim$\"+Jc8nHF]em7$F _jm$\"+XQl[JF]em7$Fdjm$\"+gL6cJF]em7%7$Fjjm$\"+!\\::@$F]em7$F_[n$\"+') RF/HF]em7$Fd[n$\"+mB\"e+$F]em7%7$Fj[n$\"+leQ_KF]em7$F_\\n$\"+6OSjGF]em 7$Fd\\n$\"+A2)f'HF]em7%7$Fj\\n$\"+i#orB$F]em7$F_]n$\"+97iyGF]em7$Fd]n$ \"+xdc#)HF]em7%7$Fj]n$\"+*[[k'GF]em7$F_^n$\"+()4M\\KF]em7$Fd^n$\"+')Rq '=$F]em7%7$Fj^n$\"+tWDbGF]em7$F__n$\"+.]`gKF]em7$Fd_n$\"+i/S%=$F]em7%7 $Fj_n$\"+dY!p@$F]em7$F_`n$\"+>[)))*GF]em7$Fd`n$\"+N&>7+$F]em7%7$Fj`n$ \"+c<>jKF]em7$F_an$\"+?xf_GF]em7$Fdan$\"+kWo\\HF]em7%7$Fjan$\"+!4Tt(GF ]em7$F_bn$\"+'Q[%QKF]em7$Fdbn$\"+R/.'=$F]em7%7$Fjbn$\"+ISz^GF]em7$F_cn $\"+Ya*RE$F]em7$Fdcn$\"+UWc\"=$F]em7%7$Fjcn$\"+Rb3jKF]em7$F_dn$\"+QRq_ GF]em7$Fddn$\"+)Q4*\\HF]em7%7$Fjdn$\"+)yg4E$F]em7$F_en$\"+)oG[&GF]em7$ Fden$\"+@b*Q&HF]em7%7$Fjen$\"+&[i2&GF]em7$F_fn$\"+\"*p-lKF]em7$Fdfn$\" +kLyzJF]em7%7$Fjfn$\"+GOHkKF]em7$F_gn$\"+[e\\^GF]em7$Fdgn$\"+KF4ZHF]em 7%7$Fjgn$\"+r8aTKF]em7$F_hn$\"+0\"[U(GF]em7$Fdhn$\"+%*)G\"yHF]em7%7$Fh dm$\"+%HkjY$F]em7$F_em$\"+IT+\"[$F]em7$Fdem$\"+qfxHNF]em7%7$Fjem$\"+/@ )3W$F]em7$F_fm$\"+?j[1NF]em7$Fdfm$\"+\\_gVNF]em7%7$Fjfm$\"+N.dNF]em7$Fdgm$\"+[7joNF]em7%7$Fjgm$\"+F8!4M$F]em7$F_hm$\"+ (4nkg$F]em7$Fdhm$\"+q<'*)e$F]em7%7$Fjhm$\"+I]ICLF]em7$F_im$\"+%RjIi$F] em7$Fdim$\"+\\w_%f$F]em7%7$Fjim$\"+0^#HQ$F]em7$F_jm$\"+>LWkNF]em7$Fdjm $\"+MG!>d$F]em7%7$Fjjm$\"+k\\IFOF]em7$F_[n$\"+gM1?LF]em7$Fd[n$\"+S=g@M F]em7%7$Fj[n$\"+R`zKF]em7$Fd\\n$\"+'>q(Qo KF]em7$Fdan$\"+QRZlLF]em7%7$Fjan$\"+k08$H$F]em7$F_bn$\"+gyBaOF]em7$Fdb n$\"+8*>=g$F]em7%7$Fjbn$\"+/NenKF]em7$F_cn$\"+?\\yzOF]em7$Fdcn$\"+;RN( f$F]em7%7$Fjcn$\"+8]()yOF]em7$F_dn$\"+7M\\oKF]em7$Fddn$\"+i))plLF]em7% 7$Fjdn$\"+i-vwOF]em7$F_en$\"+i\"=1F$F]em7$Fden$\"+&*\\opLF]em7%7$Fjen$ \"+f>bmKF]em7$F_fn$\"+lk\"3o$F]em7$Fdfn$\"+QGd&f$F]em7%7$Fjfn$\"+-J3!o $F]em7$F_gn$\"+A`GnKF]em7$Fdgn$\"+1A)GO$F]em7%7$Fjgn$\"+X3LdOF]em7$F_h n$\"+zv.!H$F]em7$Fdhn$\"+o$=RR$F]em7%7$Fhdm$\"+oP:#)QF]em7$F_em$\"+/Oz '*QF]em7$Fdem$\"+WacXRF]em7%7$Fjem$\"+y:ncQF]em7$F_fm$\"+%zvA#RF]em7$F dfm$\"+BZRfRF]em7%7$Fjfm$\"+4)ff!QF]em7$F_gm$\"+jv)H(RF]em7$Fdgm$\"+A2 U%)RF]em7%7$Fjgm$\"+,3pcPF]em7$F_hm$\"+rlDASF]em7$Fdhm$\"+W7v/SF]em7%7 $Fjhm$\"+/X4SPF]em7$F_im$\"+oG&)QSF]em7$Fdim$\"+BrJ5SF]em7%7$Fjim$\"+z Xr)z$F]em7$F_jm$\"+$zK-)RF]em7$Fdjm$\"+3Bp()RF]em7%7$Fjjm$\"+QW4VSF]em 7$F_[n$\"+MH&et$F]em7$Fd[n$\"+98RPQF]em7%7$Fj[n$\"+8['R3%F]em7$F_\\n$ \"+fD)\\p$F]em7$Fd\\n$\"+q'fvz$F]em7%7$Fj\\n$\"+5suoSF]em7$F_]n$\"+i,? 5PF]em7$Fd]n$\"+DZ99QF]em7%7$Fj]n$\"+Pu-)p$F]em7$F_^n$\"+N*>43%F]em7$F d^n$\"+MHG=SF]em7%7$Fj^n$\"+@M$oo$F]em7$F__n$\"+^R6#4%F]em7$Fd_n$\"+5% zf,%F]em7%7$Fj_n$\"+0O[[SF]em7$F_`n$\"+nPYIPF]em7$Fd`n$\"+$[)zKQF]em7% 7$Fj`n$\"+/2x%4%F]em7$F_an$\"+om<%o$F]em7$Fdan$\"+7ME\"y$F]em7%7$Fjan$ \"+Q+#*3PF]em7$F_bn$\"+Mt-qSF]em7$Fdbn$\"+(Q4w,%F]em7%7$Fjbn$\"+yHP$o$ F]em7$F_cn$\"+%Rub4%F]em7$Fdcn$\"+!RVJ,%F]em7%7$Fjcn$\"+([kY4%F]em7$F_ dn$\"+')GG%o$F]em7$Fddn$\"+O$)[\"y$F]em7%7$Fjdn$\"+O(RD4%F]em7$F_en$\" +OwS'o$F]em7$Fden$\"+pWZ&y$F]em7%7$Fjen$\"+L9M#o$F]em7$F_fn$\"+Rfg'4%F ]em7$Fdfn$\"+7BO6SF]em7%7$Fjfn$\"+wD(e4%F]em7$F_gn$\"+'zuIo$F]em7$Fdgn $\"+!or'yPF]em7%7$Fjgn$\"+>.7tSF]em7$F_hn$\"+`q#eq$F]em7$Fdhn$\"+Uyq4Q F]em7%7$Fhdm$\"+UK%zH%F]em7$F_em$\"+yIe7VF]em7$Fdem$\"+=\\NhVF]em7%7$F jem$\"+_5YsUF]em7$F_fm$\"+o_1QVF]em7$Fdfm$\"+(>%=vVF]em7%7$Fjfm$\"+$G \\5-S%F]em7%7$Fjgm$\"+v-[sTF]em 7$F_hm$\"+Xg/QWF]em7$Fdhm$\"+=2a?WF]em7%7$Fjhm$\"+yR)e:%F]em7$F_im$\"+ UBkaWF]em7$Fdim$\"+(f1hU%F]em7%7$Fjim$\"+`S]9UF]em7$F_jm$\"+nA-'R%F]em 7$Fdjm$\"+#y\"[.WF]em7%7$Fjjm$\"+7R))eWF]em7$F_[n$\"+3Ck^TF]em7$Fd[n$ \"+)y!=`UF]em7%7$Fj[n$\"+(Ga(*\\%F]em7$F_\\n$\"+L?x5TF]em7$Fd\\n$\"+W \"\\L@%F]em7%7$Fj\\n$\"+%oOX[%F]em7$F_]n$\"+O'*)f7%F]em7$Fd]n$\"+*>M*H UF]em7%7$Fj]n$\"+6p\"Q6%F]em7$F_^n$\"+4%4n\\%F]em7$Fd^n$\"+3C2MWF]em7% 7$Fj^n$\"+&*Gi-TF]em7$F__n$\"+DM!z]%F]em7$Fd_n$\"+%))o%F]em7%7$Fjan$\"+7&4Z7%F]em7$F_b n$\"+3o\"e[%F]em7$Fdbn$\"+h))RLWF]em7%7$Fjbn$\"+_C;*4%F]em7$F_cn$\"+oQ O6XF]em7$Fdcn$\"+kG$*GWF]em7%7$Fjcn$\"+hRX5XF]em7$F_dn$\"+gB2+TF]em7$F ddn$\"+5yF(>%F]em7%7$Fjdn$\"+5#H$3XF]em7$F_en$\"+5r>-TF]em7$Fden$\"+VR E,UF]em7%7$Fjen$\"+248)4%F]em7$F_fn$\"+8aR7XF]em7$Fdfn$\"+'y^rU%F]em7% 7$Fjfn$\"+]?m6XF]em7$F_gn$\"+qU'))4%F]em7$Fdgn$\"+a6Y%>%F]em7%7$Fjgn$ \"+$z4*)[%F]em7$F_hn$\"+Flh@TF]em7$Fdhn$\"+;t\\DUF]em7%7$Fhdm$\"+;Ft8Z F]em7$F_em$\"+_DPGZF]em7$Fdem$\"+#RWrx%F]em7%7$Fjem$\"+E0D)o%F]em7$F_f m$\"+UZ&Qv%F]em7$Fdfm$\"+rO(4z%F]em7%7$Fjfm$\"+d(Qvj%F]em7$F_gm$\"+6lc /[F]em7$Fdgm$\"+q'**f\"[F]em7%7$Fjgm$\"+\\(p#)e%F]em7$F_hm$\"+>b$Q&[F] em7$Fdhm$\"+#>Ij$[F]em7%7$Fjhm$\"+_MnrXF]em7$F_im$\"+;=Vq[F]em7$Fdim$ \"+rg*=%[F]em7%7$Fjim$\"+FNHIYF]em7$F_jm$\"+T<\"=\"[F]em7$Fdjm$\"+c7F> [F]em7%7$Fjjm$\"+'QtY([F]em7$F_[n$\"+#)=VnXF]em7$Fd[n$\"+i-(*oYF]em7%7 $Fj[n$\"+hPa:\\F]em7$F_\\n$\"+2:cEXF]em7$Fd\\n$\"+='Q\"HYF]em7%7$Fj\\n $\"+ehK+\\F]em7$F_]n$\"+5\"z&\\^%F]em7$F_cn$\"+UL:F\\F]em7$Fdc n$\"+QBsW[F]em7%7$Fjcn$\"+NMCE\\F]em7$F_dn$\"+M='e^%F]em7$Fddn$\"+%GnI h%F]em7%7$Fjdn$\"+%o=T#\\F]em7$F_en$\"+%e')z^%F]em7$Fden$\"+A&H^F]em7$F _em$\"+E?;W^F]em7$Fdem$\"+mQ$H>&F]em7%7$Fjem$\"+++//^F]em7$F_fm$\"+;Uk p^F]em7$Fdfm$\"+XJw1_F]em7%7$Fjfm$\"+J#GL0&F]em7$F_gm$\"+&)fN?_F]em7$F dgm$\"+W\"*yJ_F]em7%7$Fjgm$\"+B#fS+&F]em7$F_hm$\"+$*\\ip_F]em7$Fdhm$\" +m'>@D&F]em7%7$Fjhm$\"+EHY()\\F]em7$F_im$\"+!H@iG&F]em7$Fdim$\"+Xbod_F ]em7%7$Fjim$\"+,I3Y]F]em7$F_jm$\"+:7gF_F]em7$Fdjm$\"+I21N_F]em7%7$Fjjm $\"+gGY!H&F]em7$F_[n$\"+c8A$)\\F]em7$Fd[n$\"+O(fZ3&F]em7%7$Fj[n$\"+NKL J`F]em7$F_\\n$\"+\")4NU\\F]em7$Fd\\n$\"+#4G\\/&F]em7%7$Fj\\n$\"+Kc6;`F ]em7$F_]n$\"+%eov&\\F]em7$Fd]n$\"+ZJ^h]F]em7%7$Fj]n$\"+feRX\\F]em7$F_^ n$\"+d$)GG`F]em7$Fd^n$\"+c8ll_F]em7%7$Fj^n$\"+V=?M\\F]em7$F__n$\"+tB[R `F]em7$Fd_n$\"+KyMj_F]em7%7$Fj_n$\"+F?&eH&F]em7$F_`n$\"+*=Ky(\\F]em7$F d`n$\"+0p;!3&F]em7%7$Fj`n$\"+E\"R@M&F]em7$F_an$\"+!4X:$\\F]em7$Fdan$\" +M=jG]F]em7%7$Fjan$\"+g%)Gc\\F]em7$F_bn$\"+cdR<`F]em7$Fdbn$\"+4y(\\E&F ]em7%7$Fjbn$\"++9uI\\F]em7$F_cn$\"+;G%HM&F]em7$Fdcn$\"+7=^g_F]em7%7$Fj cn$\"+4H.U`F]em7$F_dn$\"+38lJ\\F]em7$Fddn$\"+en&)G]F]em7%7$Fjdn$\"+e\" 3*R`F]em7$F_en$\"+egxL\\F]em7$Fden$\"+\"*G%G.&F]em7%7$Fjen$\"+b)4(H\\F ]em7$F_fn$\"+hV(RM&F]em7$Fdfn$\"+M2te_F]em7%7$Fjfn$\"+)*4CV`F]em7$F_gn $\"+=KWI\\F]em7$Fdgn$\"+-,/E]F]em7%7$Fjgn$\"+T()[?`F]em7$F_hn$\"+va>` \\F]em7$Fdhn$\"+ki2d]F]em7%7$Fhdm$\"+k;JXbF]em7$F_em$\"++:&*fbF]em7$Fd em$\"+SLs3cF]em7%7$Fjem$\"+u%H)>bF]em7$F_fm$\"+!pLae&F]em7$Fdfm$\"+>Eb AcF]em7%7$Fjfm$\"+0x6paF]em7$F_gm$\"+fa9OcF]em7$Fdgm$\"+='yvk&F]em7%7$ Fjgm$\"+(p[)>aF]em7$F_hm$\"+nWT&o&F]em7$Fdhm$\"+S\"4zm&F]em7%7$Fjhm$\" ++CD.aF]em7$F_im$\"+k2,-dF]em7$Fdim$\"+>]ZtcF]em7%7$Fjim$\"+vC(=Y&F]em 7$F_jm$\"+*o!RVcF]em7$Fdjm$\"+/-&3l&F]em7%7$Fjjm$\"+MBD1dF]em7$F_[n$\" +I3,*R&F]em7$Fd[n$\"+5#\\0]&F]em7%7$Fj[n$\"+4F7ZdF]em7$F_\\n$\"+b/9e`F ]em7$Fd\\n$\"+mvrgaF]em7%7$Fj\\n$\"+1^!>t&F]em7$F_]n$\"+e!eLP&F]em7$Fd ]n$\"+@EIxaF]em7%7$Fj]n$\"+L`=h`F]em7$F_^n$\"+Jy2WdF]em7$Fd^n$\"+I3W\" o&F]em7%7$Fj^n$\"+<8**\\`F]em7$F__n$\"+Z=FbdF]em7$Fd_n$\"+1t8zcF]em7%7 $Fj_n$\"+,:k6dF]em7$F_`n$\"+j;i$R&F]em7$Fd`n$\"+zj&f\\&F]em7%7$Fj`n$\" ++'Gzv&F]em7$F_an$\"+kXLZ`F]em7$Fdan$\"+38UWaF]em7%7$Fjan$\"+Mz2s`F]em 7$F_bn$\"+I_=LdF]em7$Fdbn$\"+$Gn2o&F]em7%7$Fjbn$\"+u3`Y`F]em7$F_cn$\"+ !HK(edF]em7$Fdcn$\"+'G,jn&F]em7%7$Fjcn$\"+$QAyv&F]em7$F_dn$\"+#ySuM&F] em7$Fddn$\"+KikWaF]em7%7$Fjdn$\"+KwpbdF]em7$F_en$\"+Kbc\\`F]em7$Fden$ \"+lBj[aF]em7%7$Fjen$\"+H$*\\X`F]em7$F_fn$\"+NQwfdF]em7$Fdfn$\"+3-_ucF ]em7%7$Fjfn$\"+s/.fdF]em7$F_gn$\"+#pKiM&F]em7$Fdgn$\"+w&H=W&F]em7%7$Fj gn$\"+:#yit&F]em7$F_hn$\"+\\\\)*o`F]em7$Fdhn$\"+Qd'GZ&F]em7%7$Fhdm$\"+ Q65hfF]em7$F_em$\"+u4uvfF]em7$Fdem$\"+9G^CgF]em7%7$Fjem$\"+[*=c$fF]em7 $F_fm$\"+kJA,gF]em7$Fdfm$\"+$4U$QgF]em7%7$Fjfm$\"+zr!\\)eF]em7$F_gm$\" +L\\$>0'F]em7$Fdgm$\"+#4oL1'F]em7%7$Fjgm$\"+r\"Qc$eF]em7$F_hm$\"+TR?,h F]em7$Fdhm$\"+9')p$3'F]em7%7$Fjhm$\"+u=/>eF]em7$F_im$\"+Q-!y6'F]em7$Fd im$\"+$\\k#*3'F]em7%7$Fjim$\"+\\>mxeF]em7$F_jm$\"+j,=fgF]em7$Fdjm$\"+y 'Rm1'F]em7%7$Fjjm$\"+3=/AhF]em7$F_[n$\"+/.![\"eF]em7$Fd[n$\"+%oQj\"fF] em7%7$Fj[n$\"+$=7H;'F]em7$F_\\n$\"+H*HRx&F]em7$Fd\\n$\"+Sq]weF]em7%7$F j\\n$\"+!e%pZhF]em7$F_]n$\"+Kv9*y&F]em7$Fd]n$\"+&4#4$*eF]em7%7$Fj]n$\" +2[(px&F]em7$F_^n$\"+0t')fhF]em7$Fd^n$\"+/.B(4'F]em7%7$Fj^n$\"+\"z!yld F]em7$F__n$\"+@81rhF]em7$Fd_n$\"+!yE\\4'F]em7%7$Fj_n$\"+v4VFhF]em7$F_` n$\"+P6T4eF]em7$Fd`n$\"+`eu6fF]em7%7$Fj`n$\"+u!=P<'F]em7$F_an$\"+QS7jd F]em7$Fdan$\"+#y5-'eF]em7%7$Fjan$\"+3u'yy&F]em7$F_bn$\"+/Z(*[hF]em7$Fd bn$\"+dnb'4'F]em7%7$Fjbn$\"+[.KidF]em7$F_cn$\"+k<_uhF]em7$Fdcn$\"+g24# 4'F]em7%7$Fjcn$\"+d=hthF]em7$F_dn$\"+c-BjdF]em7$Fddn$\"+1dVgeF]em7%7$F jdn$\"+1r[rhF]em7$F_en$\"+1]NldF]em7$Fden$\"+R=UkeF]em7%7$Fjen$\"+.))G hdF]em7$F_fn$\"+4LbvhF]em7$Fdfn$\"+#o4.4'F]em7%7$Fjfn$\"+Y*>[<'F]em7$F _gn$\"+m@-idF]em7$Fdgn$\"+]!>w&eF]em7%7$Fjgn$\"+*on?:'F]em7$F_hn$\"+BW x%y&F]em7$Fdhn$\"+7_l))eF]em7%7$Fhdm$\"+71*oP'F]em7$F_em$\"+[/`\"R'F]e m7$Fdem$\"+)G-.W'F]em7%7$Fjem$\"+A%39N'F]em7$F_fm$\"+QE,(*='F]em7$Fd\\n$\"+9lH#H'F]em7%7$Fj\\n$\"+aS[jlF]em7$F_]n$\"+1q $\\?'F]em7$Fd]n$\"+p:))3jF]em7%7$Fj]n$\"+\"GkF>'F]em7$F_^n$\"+znlvlF]e m7$Fd^n$\"+y(>I^'F]em7%7$Fj^n$\"+l-d\"='F]em7$F__n$\"+&z]oe'F]em7$Fd_n $\"+air5lF]em7%7$Fj_n$\"+\\/AVlF]em7$F_`n$\"+61?DiF]em7$Fd`n$\"+F``FjF ]em7%7$Fj`n$\"+[v]*e'F]em7$F_an$\"+7N\"*yhF]em7$Fdan$\"+c-+wiF]em7%7$F jan$\"+#)ol.iF]em7$F_bn$\"+yTwklF]em7$Fdbn$\"+JiM7lF]em7%7$Fjbn$\"+A)4 \"yhF]em7$F_cn$\"+Q7J!f'F]em7$Fdcn$\"+M-)y]'F]em7%7$Fjcn$\"+J8S*e'F]em 7$F_dn$\"+I(>!zhF]em7$Fddn$\"+!=DiF'F]em7%7$Fjdn$\"+!ewse'F]em7$F_en$ \"+![W6='F]em7$Fden$\"+88@!G'F]em7%7$Fjen$\"+x#yq<'F]em7$F_fn$\"+$yU8f 'F]em7$Fdfn$\"+c\"*41lF]em7%7$Fjfn$\"+?%41f'F]em7$F_gn$\"+S;\"y<'F]em7 $Fdgn$\"+C&3MF'F]em7%7$Fjgn$\"+jr&yc'F]em7$F_hn$\"+(*Qc+iF]em7$Fdhn$\" +'oWWI'F]em7%7$Fhdm$\"+'3!o#z'F]em7$F_em$\"+A*>t!oF]em7$Fdem$\"+i<4coF ]em7%7$Fjem$\"+'*y>nnF]em7$F_fm$\"+7@!G$oF]em7$Fdfm$\"+T5#*poF]em7%7$F jfm$\"+Fh[;nF]em7$F_gm$\"+\")Q^$)oF]em7$Fdgm$\"+Sq%\\*oF]em7%7$Fjgm$\" +>r@nmF]em7$F_hm$\"+*)GyKpF]em7$Fdhm$\"+ivF:pF]em7%7$Fjhm$\"+A3i]mF]em 7$F_im$\"+'=z$\\pF]em7$Fdim$\"+TM%3#pF]em7%7$Fjim$\"+(*3C4nF]em7$F_jm$ \"+6\"f2*oF]em7$Fdjm$\"+E'=#)*oF]em7%7$Fjjm$\"+c2i`pF]em7$F_[n$\"+_#zj k'F]em7$Fd[n$\"+Kw\"zu'F]em7%7$Fj[n$\"+J6\\%*pF]em7$F_\\n$\"+x)3bg'F]e m7$Fd\\n$\"+))f33nF]em7%7$Fj\\n$\"+GNFzpF]em7$F_]n$\"+![E2i'F]em7$Fd]n $\"+V5nCnF]em7%7$Fj]n$\"+bPb3mF]em7$F_^n$\"+`iW\"*pF]em7$Fd^n$\"+_#4)G pF]em7%7$Fj^n$\"+R(ftf'F]em7$F__n$\"+p-k-qF]em7$Fd_n$\"+Gd]EpF]em7%7$F j_n$\"+B*4!fpF]em7$F_`n$\"+&3!*4k'F]em7$Fd`n$\"+,[KVnF]em7%7$Fj`n$\"+A qH0qF]em7$F_an$\"+')Hq%f'F]em7$Fdan$\"+I(*y\"p'F]em7%7$Fjan$\"+cjW>mF] em7$F_bn$\"+_Ob!)pF]em7$Fdbn$\"+0d8GpF]em7%7$Fjbn$\"+'H**Qf'F]em7$F_cn $\"+7251qF]em7$Fdcn$\"+3(pO#pF]em7%7$Fjcn$\"+03>0qF]em7$F_dn$\"+/#4[f' F]em7$Fddn$\"+aY,#p'F]em7%7$Fjdn$\"+ag1.qF]em7$F_en$\"+aR$pf'F]em7$Fde n$\"+(y+gp'F]em7%7$Fjen$\"+^x'Gf'F]em7$F_fn$\"+dA82qF]em7$Fdfn$\"+I')) =#pF]em7%7$Fjfn$\"+%*))R1qF]em7$F_gn$\"+96g$f'F]em7$Fdgn$\"+)*z>*o'F]e m7%7$Fjgn$\"+Pmk$)pF]em7$F_hn$\"+rLN;mF]em7$Fdhn$\"+gTB?nF]em-%&COLORG 6&F\\dm$\"\"(!\"\"$\"#&)!\"#$\"#vFif]l-%+AXESLABELSG6$%\"xG%!G-%%VIEWG 6$;$\"++++]FFjdm$\"++++D_F]em;$!++++&\\\"F]em$\"++++&>(F]em" 2 626 361 361 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 486 19 "Bernoulli Equations" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 271 6 "Theory" }}{PARA 0 "" 0 "" {TEXT 404 77 "\nSuppose that we are to solve a first order differential equation of the form" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 24 "y '(x) = F( x , y(x) ). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 403 19 "If the expression " }{TEXT -1 1 " " }{TEXT 261 15 " F( \+ x , y(x) ) " }{TEXT -1 2 " " }{TEXT 402 19 "can be expressed as" } {TEXT -1 2 " " }{TEXT 262 23 "f(x)y(x)^n - a(x)y(x) " }{TEXT -1 1 " \+ " }{TEXT 401 32 " then the equation is said to be" }{TEXT -1 1 " " } {TEXT 264 9 "Bernoulli" }{TEXT -1 2 ". " }{TEXT 400 31 " It is more co mmonly written as" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 263 35 "y ' (x) + a(x)y(x) = f(x)y(x)^n. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 399 24 "The change of variable \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 265 17 "z(x) = y(x)^(1-n)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 398 17 "or, equivalently," }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 273 21 "y(x) = z(x)^(1/(1-n))" }}{PARA 0 "" 0 " " {TEXT -1 1 "\n" }{TEXT 397 29 "leads to a linear equation in" } {TEXT -1 3 " " }{TEXT 266 4 "z(x)" }{TEXT -1 2 " ." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 272 7 "Example" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "Solve the equation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 407 2 " " }{XPPEDIT 408 0 "diff(y(x),x) = y(x)*(2-3* x*y(x));" "/-%%diffG6$-%\"yG6#%\"xGF)*&-F'6#F)\"\"\",&\"\"#F-*(\"\"$F- F)F--F'6#F)F-!\"\"F-" }}{PARA 0 "" 0 "" {TEXT 267 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 268 9 "Solution:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 405 30 "The equation m ay be written as" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 274 34 "y ' (x) + (-2x)y(x) = - 3xy(x)^2." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 406 33 "This is Bernoulli's Equa tion with" }{TEXT -1 2 " " }{TEXT 275 5 "n = 2" }{TEXT 409 1 "." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "diff_eq := diff(y(x),x) - 2*y(x) = -3*x*y(x)^2;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%(diff_eqG/,&-%%diffG6$-%\"yG6#%\"xGF-\"\"\"F*!\"#,$ *&F-F.F*\"\"#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "dsolve (diff_eq,y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$-%\"yG6#%\"xG!\" \",(F(#\"\"$\"\"##!\"$\"\"%\"\"\"*&-%$expG6#,$F(!\"#F1%$_C1GF1F1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "y(x)= 1/rhs(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG*$,(F'#\"\"$\"\"##!\"$\"\"%\" \"\"*&-%$expG6#,$F'!\"#F0%$_C1GF0F0!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 445 11 "L et us use " }{TEXT 446 6 " MAPLE" }{TEXT -1 1 " " }{TEXT 447 52 " in a step-by-step manner to obtain this solution:\n\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:= 2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "change_of_var := y(x) = z(x)^(1/(1-n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.change_of_varG/-%\"yG6#%\"xG*$-%\"zGF(!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "diff_eq2 := Dchangevar( chan ge_of_var , diff_eq , x );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)diff_ eq2G/,&*&-%\"zG6#%\"xG!\"#-%%diffG6$F(F+\"\"\"!\"\"*$F(F1F,,$*&F+F0F(F ,!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "diff_eq3 := expand (diff_eq2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)diff_eq3G/,&*&-%\"zG 6#%\"xG!\"#-%%diffG6$F(F+\"\"\"!\"\"*$F(F1F,,$*&F+F0F(F,!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "diff_eq4 := expand(z(x)^2*di ff_eq3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)diff_eq4G/,&-%%diffG6$- %\"zG6#%\"xGF-!\"\"F*!\"#,$F-!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "diff_eq4 := -diff_eq4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)diff_eq4G/,&-%%diffG6$-%\"zG6#%\"xGF-\"\"\"F*\"\"#,$F-\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 448 34 "Now w e have a linear equation in " }{TEXT 449 5 "z(x):" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "linear_ode(d iff_eq4);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7)/,&-%%diffG6$-%\"zG6#% \"xGF,\"\"\"F)\"\"#,$F,\"\"$/*&-%$expG6#-%$IntG6$F.F,F-F%F-,$*&F3F-F,F -F0/-%%DiffG6$**%\"(GF-F3F-F)F-%\")GF-F,F9/*&F3F-F)F-,&-F76$F9F,F-%#_C GF-/*&-F46#,$F,F.F-F)F-,&-F76$,$*&FJF-F,F-F0F,F-FGF-/FI,(FQ#F0F.FJ#!\" $\"\"%FGF-/F)*&-F46#,$F,!\"#F-FSF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "soln := lastEntry(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solnG/-%\"zG6#%\"xG*&-%$expG6#,$F)!\"#\"\"\",(*&-F,6#,$F)\"\" #F0F)F0#\"\"$F6F3#!\"$\"\"%%#_CGF0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "soln := subs( z(x) = y(x)^(1-n) , soln);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solnG/*$-%\"yG6#%\"xG!\"\"*&-%$expG6#,$F*!\" #\"\"\",(*&-F.6#,$F*\"\"#F2F*F2#\"\"$F8F5#!\"$\"\"%%#_CGF2F2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "soln := y(x) = 1/rhs(soln); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solnG/-%\"yG6#%\"xG*&-%$expG6#, $F)!\"#!\"\",(*&-F,6#,$F)\"\"#\"\"\"F)F7#\"\"$F6F3#!\"$\"\"%%#_CGF7F0 " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 450 148 "After plotting some solution curves and superimposing those plots on the direction field of the differential \+ equation, we will present a function, " }{TEXT 451 13 "Bernoulli_ode " }{TEXT 452 111 ", that carries out the preceding solution one step \+ at a time, printing out the principal steps along the way. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 410 8 "Graphics" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 411 103 "In this subsection we will plot som e solution curves and superimpose them on the direction field plot. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "direction_field_plot := dfieldplot( [diff_eq] , [y(x)], x = -2 \+ .. 3 , y = -6 .. 6 ,color = COLOR(RGB,0.7,0.85,0.75)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "display(direction_field_plot);" }} {PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6]dl7%7$$!+)*=Y,?!\"*$!+#)*pdJ' F*7$$!+-\"Q&)*>F*$!+=+B%o&F*7$$!+HQ1K?F*$!+#H&3?eF*7%7$$!+pa_QeF*7%7$$!+6\"ocZ\"F *$!+xNv:jF*7$$!+4.qr9F*$!+BkC%o&F*7$$!+h.X0:F*$!+#R\"y>eF*7%7$$!+n8%H@ \"F*$!+xit:jF*7$$!+j7637F*$!+BPE%o&F*7$$!+2i/U7F*$!+5D`>eF*7%7$$!+7*RX ]*!#5$!+LEq:jF*7$$!+#\\GGW*Feo$!+ntH%o&F*7$$!+;j/&y*Feo$!+u#\\\">eF*7% 7$$!+vx\"[)oFeo$!+[Ii:jF*7$$!+LFR*z'Feo$!+_pP%o&F*7$$!+1=mYrFeo$!+!*H[ =eF*7%7$$!+MU()zUFeo$!+w0N:jF*7$$!+y$y69%Feo$!+C%\\Yo&F*7$$!+&4(p*\\%F eo$!+`$Rq\"eF*7%7$$!+z_Ki/;\"F*$!+L8t:jF*7$$\"+T\\@#>\"F*$!+$y+v<'F* 7%7$$\"+r_**=9F*$!+J\"\\Uo&F*7$$\"+&**4JU\"F*$!+p3v:jF*7$$\"+Z)4^X\"F* $!+:BzxhF*7%7$$\"+oXZ#o\"F*$!+6!QUo&F*7$$\"+)[Yfo\"F*$!+*)>w:jF*7$$\"+ pm3=q'e%>F*$!+&3JUo&F*7$$\"+F)p)[>F*$!+:*odJ'F* 7$$\"+&H76)>F*$!+Ah8yhF*7%7$$\"+MO?4AF*$!+#[EUo&F*7$$\"+-!\\=@#F*$!+=N x:jF*7$$\"+Q$pTC#F*$!+jfCyhF*7%7$$\"+GA]sCF*$!+oKA%o&F*7$$\"+)>m[Z#F*$ !+Knx:jF*7$$\"+$zZs]#F*$!+0ALyhF*7%7$$\"+nPxNFF*$!+O4A%o&F*7$$\"+\\/\" zt#F*$!+k!zdJ'F*7$$\"+'\\T.x#F*$!+9Uo&F*7$ $\"+NY(4+$F*$!+63y:jF*7$$\"+TkWLIF*$!+I*e%yhF*7%7$$!+Xg#=+#F*$!+:,=%o& F*7$$!+bR<)*>F*$!+\"*>m_]F*7$$!+Di&=.#F*$!+\\SH)=&F*7%7$$!+dZ%*Qn_]F*7$$!+l/aoZ^V*Feo$!+\\qw_]F*7$$!+h/k!y*Feo$!+Aq8(=&F*7% 7$$!+7KW&*oFeo$!+i4&Ro&F*7$$!+'Hn()y'Feo$!+W6*G0&F*7$$!+)HS09(Feo$!+D$ >j=&F*7%7$$!+!*Q3(H%Feo$!+'\\ENo&F*7$$!+A(oR7%Feo$!+5cJ`]F*7$$!+#4%o*[ %Feo$!+9oc%=&F*7%7$$!+'pun!=Feo$!+U2WzcF*7$$!+?+7^8Feo$!+k8Sd]F*7$$!+$ *4vt2%y^F*7%7$$\"+$H&>rrFfs$!+W.2j]F*7$$\"+^O9)Q\"Feo$!+i\"z#oSFeo$!+l@.TbF*7%7$$\"+R\\,eiFeo$!+Uh$H0&F*7$$ \"+LSctjFeo$!+kf!Ro&F*7$$\"+OqTo&F*7$$\"+2!oD>\"F*$!+fh_XbF*7%7 $$\"+()G[=9F*$!+5=p_]F*7$$\"+zBiB9F*$!+'H]To&F*7$$\"+4\")Rb9F*$!+wO*ea &F*7%7$$\"+&=U?o\"F*$!+iWn_]F*7$$\"+r)yjo\"F*$!+Ww;%o&F*7$$\"+@-L=F*$!+dOm_]F*7$$\"+5QC\\>F*$!+\\%yTo&F*7$$\"+RJK \")>F*$!+`iKYbF*7%7$$\"+`T()3AF*$!+vkl_]F*7$$\"+$[y@@#F*$!+Jc=%o&F*7$$ \"+=_NWAF*$!+fUYYbF*7%7$$\"+(y2AZ#F*$!+g9l_]F*7$$\"+R1;vCF*$!+Y1>%o&F* 7$$\"+%*RT2DF*$!+YDdYbF*7%7$$\"+Jw]NFF*$!+@yk_]F*7$$\"+&ew\"QFF*$!+&G% >%o&F*7$$\"+%y\"\\qFF*$!+y(fma&F*7%7$$\"+vDy)*HF*$!+(4XE0&F*7$$\"+Ju@, IF*$!+4q>%o&F*7$$\"+)f$eLIF*$!+_:tYbF*7%7$$!+1`M-?F*$!+79e_]F*7$$!+%pa w*>F*$!++G5@WF*7$$!+_(f:.#F*$!+YZTcXF*7%7$$!+@EaR6U%F*7$$!+b()>oRD0&F* 7$$!+?<]q9F*$!+:]9@WF*7$$!+#*[w/:F*$!+rj$fb%F*7%7$$!+0,S97F*$!+$p%\\_] F*7$$!+DDl17F*$!+>&*=@WF*7$$!+./@T7F*$!+DoabXF*7%7$$!+f!pJ_*Feo$!+v\"3 C0&F*7$$!+X$*>C%*Feo$!+PgF@WF*7$$!+s:Mu(*Feo$!+i5&\\b%F*7%7$$!+^$y0\"p Feo$!+$p.A0&F*7$$!+d@jtnFeo$!+>0[@WF*7$$!+JNyJrFeo$!+1x#Rb%F*7%7$$!+D( [:K%Feo$!+Va]^]F*7$$!+()Q]*4%Feo$!+p(y@U%F*7$$!+9BNvWFeo$!+Y1x^XF*7%7$ $!+%[p(o=Feo$!+Ee([/&F*7$$!+K_7*G\"Feo$!+'Q3)GWF*7$$!+_.\\Nx\\*))Feo$!+hII@WF*7$$ \"+y'f(***)Feo$!+^6Q_]F*7$$\"+4,w0$*Feo$!+i_g7\\F*7%7$$\"+I]%Q:\"F*$!+ PA?@WF*7$$\"+YW%>;\"F*$!+v>[_]F*7$$\"+C+2$>\"F*$!+ygP8\\F*7%7$$\"+YBv< 9F*$!+#)>:@WF*7$$\"+?HNC9F*$!+IA`_]F*7$$\"+U#3eX\"F*$!+CU&Q\"\\F*7%7$$ \"+ecU\"o\"F*$!+qL7@WF*7$$\"+)R&*po\"F*$!+U3c_]F*7$$\"+#)on=F*$!+[b5@WF*7$$\"+&4x(\\>F*$!+k'yD0&F*7$$\"+MLi\" )>F*$!+@bT9\\F*7%7$$\"+8VS3AF*$!+,P4@WF*7$$\"+B$[E@#F*$!+60f_]F*7$$\"+ F*>YC#F*$!+QUf9\\F*7%7$$\"+/zyrCF*$!+Ha3@WF*7$$\"+A0evCF*$!+$y)f_]F*7$ $\"+;2l2DF*$!+YVt9\\F*7%7$$\"+.\"G^t#F*$!+E%z5U%F*7$$\"+8hbQFF*$!+'y/E 0&F*7$$\"+teqqFF*$!+Kr%[\"\\F*7%7$$\"+FjV)*HF*$!+K\\2@WF*7$$\"+zOc,IF* $!+!G4E0&F*7$$\"+-!zP.$F*$!+y)R\\\"\\F*7%7$$!+m?7.?F*$!+DP'4U%F*7$$!+M z(o*>F*$!+$fi&*y$F*7$$!+/`6J?F*$!+3;(*y$F*7$$!+\"es/C\"F*$!+G'eK#RF*7%7$$!+X/`R&* Feo$!+npl?WF*7$$!+fz$yS*Feo$!+_$p)*y$F*7$$!+Na)[w*Feo$!+-\")[ARF*7%7$$ !+^CWF*7$$!+,-7jSFeo$!+(eh9z$F*7$$!+bb#QX%Feo$!+(G (\\=RF*7%7$$!+L8xd>Feo$!+n;o2WF*7$$!+$QB,?\"Feo$!+^Y%G!QF*7$$!+b#y\"z; Feo$!+oi16RF*7%7$$\"+YKF<^Ffs$!+O2RN_QFeo$!+bO Y=WF*7$$\"+6^z0TFeo$!+w`vsUF*7%7$$\"+`V<YS9kFe o$!+pW;?WF*7$$\"+7_s*p'Feo$!+%H\"*yF%F*7%7$$\"+`%fw())Feo$!+pr\"**y$F* 7$$\"+:u2\"F*$!+>x#4G%F*7%7$$ \"+F)fmT\"F*$!+@(\\'*y$F*7$$\"+RaWD9F*$!+)fw3U%F*7$$\"+)p>kX\"F*$!+'Gw :G%F*7%7$$\"+-N]!o\"F*$!+Q!*f*y$F*7$$\"+av\"zo\"F*$!+\"GF4U%F*7$$\"+WS >>F*$!+iuc*y$F*7$$\"+?[d]>F*$!+c)e4U%F*7$ $\"+y82#)>F*$!+rZL#G%F*7%7$$\"+Z9q2AF*$!+qka*y$F*7$$\"+*=^L@#F*$!+[)z4 U%F*7$$\"+R^,XAF*$!+*evDG%F*7%7$$\"+V(f6Z#F*$!+7=`*y$F*7$$\"+$o3iZ#F*$ !+1X*4U%F*7$$\"+PU+3DF*$!+STw#G%F*7%7$$\"+*HgXt#F*$!+t6_*y$F*7$$\"+F*$!+1\"o!eJF*7$$!+^\\SI?F*$!+Y#=@H$F*7%7$$!+G6'=u\"F*$!+kQ C*y$F*7$$!+#3B=t\"F*$!+gX7eJF*7$$!+!=now\"F*$!+%[a.:F*$!+^$o7H$F*7%7$$!+$)>s<7 F*$!+?6+*y$F*7$$!+Z1L.7F*$!+/tOeJF*7$$!+u>HR7F*$!+Ihe!H$F*7%7$$!+x>al& *Feo$!+9Kq)y$F*7$$!+Fk#=Q*Feo$!+5_meJF*7$$!+/ou\\(*Feo$!+t4c*G$F*7%7$$ !+I'4!ppFeo$!+/:+)y$F*7$$!+y3?:nFeo$!+@pOfJF*7$$!+Ifc(4(Feo$!+Qg&yG$F* 7%7$$!+?,>:WFeo$!+w,j&y$F*7$$!+#\\ie+%Feo$!+[#Q<;$F*7$$!+O#G%>WFeo$!+% )\\`%G$F*7%7$$!+hkN)3#Feo$!+ts%[w$F*7$$!+b#Q&p5Feo$!+^6_#=$F*7$$!+APT$ f\"Feo$!+4R.yKF*7%7$$\"+Bo!R^$Ffs$!+0'yk?$F*7$$\"+)\\sQv\"Feo$!+>)*)3u $F*7$$\"+_acG6$e$F*7%7$$\"+N/<^MFeo$!+iq)G;$F*7$$\"+T1Dfj$F*7%7$$\"+A1UyhFeo$!+;/ifJF*7$$\"+]$ eJX'Feo$!+3![xy$F*7$$\"+vc#3s'Feo$!+jA^VOF*7%7$$\"+^f8]))Feo$!+Q\"e(eJ F*7$$\"+<4gW!*Feo$!+'G5')y$F*7$$\"+6gaI$*Feo$!+Z$4kk$F*7%7$$\"+SIP]6F* $!+L6TeJF*7$$\"+OkTl6F*$!+\"Hd*)y$F*7$$\"+\"R+]>\"F*$!+Dq#zk$F*7%7$$\" +u/#\\T\"F*$!+nyBeJF*7$$\"+#z%=F9F*$!+d08*y$F*7$$\"+$[)Qd9F*$!+))*e)[O F*7%7$$\"+**[.z;F*$!+J\"R\"eJF*7$$\"+dhQ*o\"F*$!+$HH#*y$F*7$$\"+BV,?F*$!+'fx!eJF*7$$\"+:b%=&>F*$!+G3H*y$F*7$$ \"+mDy#)>F*$!+**G%*\\OF*7%7$$\"+,#\\$*>F*$!+tAqEDF*7$$!+QY;H?F*$!+%4r$fEF*7%7$$!+]HLW\"F*$!+EuOFDF*7$$!+0\"GsB\"F*$!+-`@dEF*7%7$$!+')Q\\5' *Feo$!+?J=cJF*7$$!+=X(oL*Feo$!+5u-GDF*7$$!+\"GzKs*Feo$!+I&=el#F*7%7$$! +_=gIqFeo$!+;vjaJF*7$$!+c'3Ol'Feo$!+9IdHDF*7$$!+1XygqFeo$!+`Of`EF*7%7$ $!+lK!=^%Feo$!+v_]\\JF*7$$!+Z$\\#4RFeo$!+b_qMDF*7$$!+TW\"*fVFeo$!+Ynt \\EF*7%7$$!+B&=\"yAFeo$!+&4B'4JF*7$$!+E>w(z)Ffs$!+NueuDF*7$$!+&f!>h9Fe o$!+$yv%[EF*7%7$$\"+]m()4:Ffs$!+/J67EF*7$$\"+:bFa>Feo$!+Eu4sIF*7$$\"+5 uU.=Feo$!+k#4%=HF*7%7$$\"+.UiULFeo$!+@F9PDF*7$$\"+tozDSFeo$!+4y1ZJF*7$ $\"+o\\b&>%Feo$!+u*>X*HF*7%7$$\"+dw%>6'Feo$!+,$G,`#F*7$$\"+:8j>lFeo$!+ HA3aJF*7$$\"+=7McnFeo$!+J\"F*$!+TVx8IF*7%7$$\"+uW!>T\"F*$!+e*zq_# F*7$$\"+#z+-V\"F*$!+s08dJF*7$$\"+fY0f9F*$!+<p\"F*$!+\\,NdJF*7$$\"+D!G9s\"F*$!+F1@;IF*7%7$$\"+%= &oS>F*$!+0MsEDF*7$$\"+i;0a>F*$!+Dr[dJF*7$$\"+7+,%)>F*$!+IG\"p,$F*7%7$$ \"+,qj/AF*$!+oAjEDF*7$$\"+NcT;AF*$!+i#yv:$F*7$$\"+cssYAF*$!+d3WkdJF*7$$\"+cr`4DF*$!+QA&y,$ F*7%7$$\"+&p$3KFF*$!+eB_EDF*7$$\"+@0gTFF*$!+s\")odJF*7$$\"+(G8Cx#F*$!+ <<==IF*7%7$$\"+=&ec*HF*$!+Ox[EDF*7$$\"+)[TV+$F*$!+%zAx:$F*7$$\"+'RQ`.$ F*$!+/:X=IF*7%7$$!+n]t5?F*$!+LIEDDF*7$$!+L\\E*)>F*$!+.'*y&*=F*7$$!+G%) pE?F*$!+eNjD?F*7%7$$!+3.>\\\"F*$ !+Xfe(*=F*7$$!+na7L7F*$!+>@^A?F*7%7$$!+E-v(p*Feo$!+eLq@DF*7$$!+y\"='\\ #*Feo$!+y#\\$**=F*7$$!+iVyq'*Feo$!+F*[1-#F*7%7$$!+;`I[rFeo$!+2gk0f`'Feo$!+HmS.>F*7$$!+^+T))pFeo$!+_8-=?F*7%7$$!+$*)oto%Feo$!+>#\\ []#F*7$$!+>PoLPFeo$!+F*7$$!+r*[nC%Feo$!+;%Q],#F*7%7$$!+tV/EDFeo$! +#eV(HCF*7$$!+FM]=jFfs$!+a!48*>F*7$$!+(p1.F\"Feo$!+$42%H?F*7%7$$!).]8a Feo$!+YJuR?F*7$$\"+$=)Rf@Feo$!+!\\48Q#F*7$$\"+GL0e=Feo$!+7A&4C#F*7%7$$ \"+uG))\\JFeo$!+6t%>#>F*7$$\"+-#Q&=UFeo$!+D`5*\\#F*7$$\"+p1x(G%Feo$!+! H(3UBF*7%7$$\"+D7i&)fFeo$!+!GS[!>F*7$$\"+Zx&fk'Feo$!+cB@;DF*7$$\"+_OT@ oFeo$!+Bj.kBF*7%7$$\"+iv`5()Feo$!+kU*)**=F*7$$\"+1$*>%=*Feo$!+t$e6_#F* 7$$\"+(eB_S*Feo$!+&*3WsBF*7%7$$\"+bNZR6F*$!+Sp%y*=F*7$$\"+@fJw6F*$!+'p 0K_#F*7$$\"+$354?\"F*$!+W)enP#F*7%7$$\"+)4$*fS\"F*$!+%)>\"o*=F*7$$\"+o @6O9F*$!+_1CCDF*7$$\"+v(pAY\"F*$!+REOzBF*7%7$$\"+-+[r;F*$!+k$=i*=F*7$$ \"+a5%pp\"F*$!+sU$[_#F*7$$\"+')*oTs\"F*$!+?m4\"Q#F*7%7$$\"+G_MO>F*$!+u p%e*=F*7$$\"+=;Re>F*$!+ic?DDF*7$$\"+LvR')>F*$!+#fJBQ#F*7%7$$\"+px!3?#F *$!+3%*f&*=F*7$$\"+n[C?AF*$!+GKXDDF*7$$\"+)\\T)[AF*$!+YZD$Q#F*7%7$$\"+ wZ*\\Y#F*$!+9iU&*=F*7$$\"+]OP#[#F*$!+AkiDDF*7$$\"+TRV6DF*$!+7/(RQ#F*7% 7$$\"+c])*GFF*$!+a.I&*=F*7$$\"+g\"*pWFF*$!+#G_d_#F*7$$\"+&*H8uFF*$!+07 a%Q#F*7%7$$\"+A+$G*HF*$!+Rg?&*=F*7$$\"+%)*pr+$F*$!+(fYe_#F*7$$\"+`6\"p .$F*$!+Bp+&Q#F*7%7$$!+AX%3-#F*$!+!3\\2*=F*7$$!+ya:z>F*$!+ic9n7F*7$$!+l 2m??F*$!+]Il*Q\"F*7%7$$!+,tug%)=F*7$$!+C:\"o<\"F *$!+l/qt7F*7$$!+5q?B7F*$!+ytk&Q\"F*7%7$$!+Ve!e*)*Feo$!+z]/y=F*7$$!+hDc ^!*Feo$!+j'\\)z7F*7$$!+1n!fa*Feo$!+ra.%Q\"F*7%7$$!+\"p13S(Feo$!+O_&['= F*7$$!+LQ\"F*7%7$$!+:#)33]F eo$!+\\86I=F*7$$!+(RkHT$Feo$!+$R$yF8F*7$$!+yz%*>SFeo$!+roo)Q\"F*7%7$$! +VObfFFeo$!+G(o$=Feo$!+@w^![\"F*7$$\"+z;(GI#Feo$!+@rPx;F*7$$\"+IG.k=Feo$!+%Q T(f:F*7%7$$\"+1h,?GFeo$!+s#=3M\"F*7$$\"+q\\S[XFeo$!+qk2<=F*7$$\"+[*[AU %Feo$!+!)=6i;F*7%7$$\"+7cy>dFeo$!+*y6uH\"F*7$$\"+gLz6pFeo$!+aH[g=F*7$$ \"+WB)p%pFeo$!+QU\"Gq\"F*7%7$$\"+Te<.&)Feo$!+ekp\"G\"F*7$$\"+F5c\"R*Fe o$!+%G)>w=F*7$$\"+gj&)3&*Feo$!+3L$3s\"F*7%7$$\"+YXvA6F*$!+zyiu7F*7$$\" +I\\.$>\"F*$!+joE$)=F*7$$\"+G(=&47F*$!+U&3/t\"F*7%7$$\"+@/2#R\"F*$!+^O \"4F\"F*7$$\"+X[.]9F*$!+\"4\")p)=F*7$$\"+D?dp9F*$!+^#4it\"F*7%7$$\"+!3 %ef;F*$!+M\"Q(o7F*7$$\"+wp$)3c+u\"F*7% 7$$\"+Q_(f#>F*$!+)yftE\"F*7$$\"+3;wo>F*$!+a\\`!*=F*7$$\"+F^&>*>F*$!+iw xU#F*$!+qMVm7F*7$$\"+C(G%HAF*$!+s7Y\"*=F*7$$\"+tsz`AF *$!+StzW:s#F*$!+gjIl7F*7$$\"+*\\k@v#F*$!+#Q)e#*=F*7 $$\"+[1?yFF*$!+1WeZF* $!+(o'G*e'Feo7$$!+'=w'**>F*$!+-'))o^(Feo7%7$$!+4&>pz\"F*$!+4%>$G7F*7$$ !+,Zww;F*$!+'QuTm'Feo7$$!+2Z/Kje09F*$!+H2hrnFeo7$$!+q,Aj9F*$!+Kb0LvFeo7%7$$!+%GW&)G\"F*$!+Pwl,7F *7$$!+Y$3D8\"F*$!+-@zIpFeo7$$!+x&zF>\"F*$!+%)))yjvFeo7%7$$!+8G`P5F*$!+ %egt<\"F*7$$!+t-/s&)Feo$!+PEwtrFeo7$$!+9(Q??*Feo$!+Y:nGwFeo7%7$$!+m7&e )yFeo$!+WElR6F*7$$!+U#f$)z&Feo$!+N?%3b(Feo7$$!+'e51X'Feo$!+D&4sv(Feo7% 7$$!+7$e-S&Feo$!+/vC#3\"F*7$$!++Vz?IFeo$!+LM*[7)Feo7$$!+8CYwOFeo$!+zx4 &*zFeo7%7$$!+,mcuGFeo$!+9(\\C+\"F*7$$!*:\"GLGFeo$!+K8(G#*)Feo7$$!+![Ss ,*Ffs$!+q(3SQ)Feo7%7$$!*tx2a#Feo$!+HCL.\"*Feo7$$\"+`4MfBFeo$!+Vg.W)*Fe o7$$\"+9v4K=Feo$!+*QV'**))Feo7%7$$\"+\\\")>oCFeo$!+HEUn#)Feo7$$\"+FHA+ \\Feo$!+%e%*z1\"F*7$$\"+ojK*\\%Feo$!+4=,G%*Feo7%7$$\"+(*o=U_Feo$!+\"o! )zk(Feo7$$\"+v?R*Q(Feo$!+z(Q*H6F*7$$\"+rfo9rFeo$!+2Mnk)*Feo7%7$$\"+;ls =!)Feo$!+k_\\OsFeo7$$\"+_.,w)*Feo$!+@t3r6F*7$$\"+Cr$pq*Feo$!+#o&\\=5F* 7%7$$\"+a\"F*7$$\"++(o%H7F*$!+&> *3T5F*7%7$$\"+ h&)[\"F*$!+nt4d5F*7%7$$\"+5;mA;F*$!+>7e#o'Feo7$$\"+Y%fdu\"F*$!+D(ykA\" F*7$$\"+s>=[J@+#F*$ !+8;#F*$!+&RH\\a'Feo7$$ \"+uMtfAF*$!+3RCS7F*7$$\"+8S$*oAF*$!+53!R3\"F*7%7$$\"+>!z!HCF*$!++$zF] 'Feo7$$\"+2%*G=DF*$!+<*eWC\"F*7$$\"+=<#*HDF*$!+V=0*3\"F*7%7$$\"+')\\4' p#F*$!+Qq-rkFeo7$$\"+I#*exFF*$!+VTjZ7F*7$$\"+))GA\"z#F*$!+**p;$4\"F*7% 7$$\"+RX_iHF*$!+8-eYkFeo7$$\"+oaZPIF*$!+E)y+D\"F*7$$\"+\\/y_IF*$!+)4;l 4\"F*7%7$$!+06nF@F*$!+[%*z@RFeo7$$!+&*)GB(=F*$!+w+*RR#Feo7$$!+Y%pb$>F* $!+xQue>Feo7%7$$!+'eTa'=F*$!+-'4h#QFeo7$$!+CEC3;F*$!+B*z'*[#Feo7$$!+/% ))3n\"F*$!+\\&Gu+#Feo7%7$$!+&p(4.;F*$!+9PXGPFeo7$$!+D2FW8F*$!+5eL(e#Fe o7$$!+IaDEMFeo 7$$!+Sb2JbFeo$!+0T`*)GFeo7$$!+%HAn7'Feo$!+])>\">AFeo7%7$$!+vr]CbFeo$!+ E:TBLFeo7$$!+Paa'*GFeo$!+)*zP#*HFeo7$$!+trv#[$Feo$!+Q.mvAFeo7%7$$!+Y?[ %*GFeo$!+Yp.?KFeo7$$!*qETj#Feo$!+yDv&4$Feo7$$!+N/H&R)Ffs$!+?,MLBFeo7%7 $$!*FY/j#Feo$!+\"=ik6$Feo7$$\"+2yIoBFeo$!+VtK*>$Feo7$$\"+)=>H!=Feo$!+z 2)>R#Feo7%7$$\"+Yk!)pBFeo$!+X4-8IFeo7$$\"+IYh)*\\Feo$!+z&oFI$Feo7$$\"+ &)>bWWFeo$!+@RR^CFeo7%7$$\"+>*eS+&Feo$!+1[/5HFeo7$$\"+`+_FwFeo$!+=Zu0M Feo7$$\"+g%Q6DFeo7%7$$\"+TsoRwFeo$!+=z&y!GFeo7$$\"+j\\]D5 F*$!+1;$z]$Feo7$$\"+N#p_s*Feo$!+\"\\_#)H\"=F*$!+h#Gn!QFeo7$$\"+66)Rw\"F*$!+*4XJv# Feo7%7$$\"+dG]>=F*$!+>*fHT#Feo7$$\"+*)RBv?F*$!+0'HG!RFeo7$$\"+8jiF?F*$ !+i*pI\"GFeo7%7$$\"+a]n$3#F*$!+L3+>BFeo7$$\"+$extL#F*$!+\"p)y'*RFeo7$$ \"+`y=\"H#F*$!+x$HC(GFeo7%7$$\"+Es%zM#F*$!+7(ytA#Feo7$$\"+,7U*f#F*$!+8 3T)3%Feo7$$\"+k$oYb#F*$!+>O1JHFeo7%7$$\"+\\2J7EF*$!+l!f#Q@Feo7$$\"+nMP hGF*$!+f/`xTFeo7$$\"+752=GF*$!+'4F)))HFeo7%7$$\"+dnvwGF*$!+x!y<0#Feo7$ $\"+\\KCBJF*$!+Z9,kUFeo7$$\"+2%*R\"3$F*$!+(R*eXIFeo7%7$$!+16nF@F*$\"+[ +*RR#Feo7$Fj_v$\"+w$*z@RFeo7$F_`v$\"+(eXqN%Feo7%7$Fe`v$\"+$*)z'*[#Feo7 $Fj`v$\"+J&4h#QFeo7$F_av$\"+:4O3VFeo7%7$Feav$\"+ydL(e#Feo7$Fjav$\"+YOX GPFeo7$F_bv$\"+#HvyD%Feo7%7$Febv$\"+)>8no#Feo7$Fjbv$\"+Ei2HOFeo7$F_cv$ \"+\"*[o0UFeo7%7$Fecv$\"+:%Feo7%7$Fedv$\"+kS`*)GFeo7$Fjdv$\"+g`DEMFeo7$$!+$HAn7'Fe o$\"+>'pm4%Feo7%7$Feev$\"+`zP#*HFeo7$Fjev$\"+r9TBLFeo7$F_fv$\"+L\"H,/% Feo7%7$Fefv$\"+IDv&4$Feo7$Fjfv$\"+%*o.?KFeo7$F_gv$\"+`$\\C)RFeo7%7$Feg v$\"+\"HF$*>$Feo7$Fjgv$\"+L@Y;JFeo7$$\"+(=>H!=Feo$\"+'p3Q#RFeo7%7$Fehv $\"+D&oFI$Feo7$Fjhv$\"+**3-8IFeo7$F_iv$\"+bbRkQFeo7%7$Feiv$\"+gYu0MFeo 7$Fjiv$\"+kZ/5HFeo7$$\"+fx1FFeo7$$\"+dBVO7F*$\"+Q.\\$o$Feo7%7$Fe\\w$\"+4wq3PFeo7$F j\\w$\"+:=32EFeo7$$\"+K-D+:F*$\"+TB'Hi$Feo7%7$Fe]w$\"+\">Gn!QFeo7$$\"+ )>#)H\"=F*$\"+L714DFeo7$$\"+76)Rw\"F*$\"+)QWEc$Feo7%7$Fe^w$\"+L&HG!RFe o7$Fj^w$\"+\"*)fHT#Feo7$F__w$\"+D&>F]$Feo7%7$$\"+`]n$3#F*$\"+<')y'*RFe o7$Fj_w$\"+33+>BFeo7$$\"+_y=\"H#F*$\"+8,OVMFeo7%7$$\"+Ds%zM#F*$\"+O2T) 3%Feo7$Fj`w$\"+)oytA#Feo7$$\"+j$oYb#F*$\"+tes%Q$Feo7%7$$\"+[2J7EF*$\"+ \"QIv<%Feo7$$\"+oMPhGF*$\"+V!f#Q@Feo7$F_bw$\"+(RipK$Feo7%7$Febw$\"+n8, kUFeo7$Fjbw$\"+d!y<0#Feo7$$\"+1%*R\"3$F*$\"+(4+-F$Feo7%7$$!+WJc`?F*$\" +UmG*e'Feo7$$!+coVY>F*$\"+t\"3eB\"F*7$$!+&=w'**>F*$\"+#)z/V6F*7%7$Fe\\ u$\"+UV$G7F*7$$!+3Z/K%3b(Feo7$$!+Q#f$)z&Feo$\"+PElR6F*7$$!+#e51X'Feo$\"+*)e,>6F*7%7$ $!+:$e-S&Feo$\"+&R$*[7)Feo7$$!+(H%z?IFeo$\"+)\\ZA3\"F*7$$!+5CYwOFeo$\" +kqA&4\"F*7%7$Febu$\"+)GrG#*)Feo7$Fjbu$\"+3(\\C+\"F*7$$!+v/CoCFeo$\"+yX*z1\"F*7$$\"+HHA+\\Feo$\"+!f AuE)Feo7$F_eu$\"+&*Feo7%7$$\"+%*o=U_Feo$\"+t(Q*H6F*7$$\"+y?R*Q(Feo $\"+W1)zk(Feo7$F_fu$\"+B]p#3*Feo7%7$$\"+6ls=!)Feo$\"+:t3r6F*7$$\"+d.,w )*Feo$\"+E_\\OsFeo7$$\"+Dr$pq*Feo$\"+;;Ti()Feo7%7$$\"+` \"F*7$$\"+Bx:Q7F*$\"+J2OrpFeo7$F_hu$\"+![wk`)Feo7%7$Fehu$\"+\\i)[@\"F* 7$Fjhu$\"+$)e])z'Feo7$F_iu$\"+oZRw$)Feo7%7$$\"+4;mA;F*$\"+?(ykA\"F*7$$ \"+Z%fdu\"F*$\"+v6e#o'Feo7$$\"+t>=[%)=F*7$F_[t$\"+ftCsSFeo$\"+ly?pdFeo$\"+[H[g=F*7$$\"+iLz6pFeo$\"+%y6uH\"F*7$F_bt$\"++0 3b9F*7%7$$\"+Re<.&)Feo$\"+y#)>w=F*7$$\"+H5c\"R*Feo$\"+akp\"G\"F*7$F_ct $\"+I91P9F*7%7$Fect$\"+eoE$)=F*7$Fjct$\"+uyiu7F*7$F_dt$\"+&>'[F9F*7%7$ Fedt$\"+'3\")p)=F*7$Fjdt$\"+YO\"4F\"F*7$F_et$\"+([&o@9F*7%7$$\"+zSef;F *$\"+.m:*)=F*7$$\"+xp$)3F*$\"+\\\\`!*=F*7$$\"+4;wo>F*$\"+$yftE\"F*7$$\"+G^&>*>F*$\"+ wq6:9F*7%7$Fegt$\"+n7Y\"*=F*7$Fjgt$\"+lMVm7F*7$F_ht$\"+(R(489F*7%7$Feh t$\"+GH6#*=F*7$Fjht$\"+/=yl7F*7$F_it$\"+6Da69F*7%7$Feit$\"+x$)e#*=F*7$ Fjit$\"+bjIl7F*7$F_jt$\"+J.J59F*7%7$Fejt$\"+4d%H*=F*7$Fjjt$\"+B!\\\\E \"F*7$F_[u$\"+U3J49F*7%7$$!+o]t5?F*$\"+)f*y&*=F*7$Fjcr$\"+GIEDDF*7$F_d r$\"+t!>aR#F*7%7$Fedr$\"+:08'*=F*7$Fjdr$\"+6@#\\_#F*7$F_er$\"+fO>'R#F* 7%7$Feer$\"+Mxm'*=F*7$Fjer$\"+#*[QCDF*7$$!+5/9)\\\"F*$\"+jr>(R#F*7%7$F efr$\"+Sfe(*=F*7$Fjfr$\"+'omM_#F*7$F_gr$\"+70a)R#F*7%7$$!+F-v(p*Feo$\" +t#\\$**=F*7$$!+x\"='\\#*Feo$\"+`Lq@DF*7$F_hr$\"+/PS+CF*7%7$$!+<`I[rFe o$\"+CmS.>F*7$$!+\">0f`'Feo$\"+-gkF*7$$!+F*7$$!+.M]=jFfs$\"+xNuHCF*7$$!+&p1.F\"Feo$\"+Qbk\" R#F*7%7$$!)/]8aFeo$\"+%[48Q#F*7$$\"+%=)Rf@Feo$\"+UJuR?F*7$F_\\s$\"+?/5 !=#F*7%7$$\"+sG))\\JFeo$\"+?`5*\\#F*7$$\"+/#Q&=UFeo$\"+1t%>#>F*7$$\"+q 1x(G%Feo$\"+T`'*y?F*7%7$$\"+C7i&)fFeo$\"+]B@;DF*7$$\"+[x&fk'Feo$\"+w-% [!>F*7$F_^s$\"+4j,d?F*7%7$$\"+hv`5()Feo$\"+o$e6_#F*7$$\"+2$*>%=*Feo$\" +eU*)**=F*7$$\"+)eB_S*Feo$\"+O\"o*=F*7$$\"+u(p AY\"F*$\"+#***oT?F*7%7$Feas$\"+nU$[_#F*7$Fjas$\"+f$=i*=F*7$F_bs$\"+6g& *R?F*7%7$Febs$\"+dc?DDF*7$Fjbs$\"+pp%e*=F*7$F_cs$\"+R5sQ?F*7%7$Fecs$\" +BKXDDF*7$Fjcs$\"+.%*f&*=F*7$F_ds$\"+&)yzP?F*7%7$Feds$\"+A3P?F*7%7$Fees$\"+xAvDDF*7$Fjes$\"+\\.I&*=F*7$F _fs$\"+E9^O?F*7%7$Fefs$\"+#fYe_#F*7$Fjfs$\"+Ng?&*=F*7$F_gs$\"+5d/O?F*7 %7$Fe_q$\"+oAqEDF*7$Fj_q$\"+_#3v:$F*7$F_`q$\"+J%R[-$F*7%7$Fe`q$\"+]z#o _#F*7$Fj`q$\"+qDQdJF*7$F_aq$\"+(*zNDIF*7%7$Feaq$\"+Dl-FDF*7$Fjaq$\"+&* R=dJF*7$F_bq$\"+iY/EIF*7%7$Febq$\"+@uOFDF*7$Fjbq$\"+*4Vo:$F*7$F_cq$\"+ B_*p-$F*7%7$Fecq$\"+0u-GDF*7$Fjcq$\"+:J=cJF*7$F_dq$\"+'*>RGIF*7%7$$!+` =gIqFeo$\"+4IdHDF*7$$!+b'3Ol'Feo$\"+6vjaJF*7$$!+0XygqFeo$\"+sohIIF*7%7 $$!+mK!=^%Feo$\"+]_qMDF*7$$!+Y$\\#4RFeo$\"+q_]\\JF*7$$!+SW\"*fVFeo$\"+ zPZMIF*7%7$$!+D&=\"yAFeo$\"+IueuDF*7$$!+7>w(z)Ffs$\"+!4B'4JF*7$$!+$f!> h9Feo$\"+UZtNIF*7%7$$\"+Mm()4:Ffs$\"+?u4sIF*7$$\"+Feo$\"++J67EF*7 $$\"+6uU.=Feo$\"+i7!ew#F*7%7$$\"+-UiULFeo$\"+/y1ZJF*7$$\"+uozDSFeo$\"+ ;F9PDF*7$F_iq$\"+^0p*o#F*7%7$$\"+cw%>6'Feo$\"+CA3aJF*7$$\"+;8j>lFeo$\" +'HG,`#F*7$F_jq$\"+%z[un#F*7%7$Fejq$\"+4x(f:$F*7$Fjjq$\"+6GBGDF*7$F_[r $\"+B$HGn#F*7%7$Fe[r$\"+ceucJF*7$Fj[r$\"+kYYFDF*7$F_\\r$\"+%=O/n#F*7%7 $Fe\\r$\"+n08dJF*7$Fj\\r$\"+`*zq_#F*7$F_]r$\"+3)y*oEF*7%7$Fe]r$\"+W,Nd JF*7$Fj]r$\"+w.'o_#F*7$F_^r$\"+**)**zm#F*7%7$Fe^r$\"+?r[dJF*7$Fj^r$\"+ +MsEDF*7$F__r$\"+&p(HnEF*7%7$Fe_r$\"+d#yv:$F*7$Fj_r$\"+jAjEDF*7$F_`r$ \"+o'pnm#F*7%7$Fe`r$\"+M>kdJF*7$Fj`r$\"+'eol_#F*7$F_ar$\"+)Gejm#F*7%7$ Fear$\"+n\")odJF*7$Fjar$\"+aB_EDF*7$F_br$\"+4)Ggm#F*7%7$Febr$\"+*yAx:$ F*7$Fjbr$\"+Jx[EDF*7$F_cr$\"+@!fdm#F*7%7$Fe[p$\"+,\"o!eJF*7$Fj[p$\"+8. I*y$F*7$F_\\p$\"+t,DbOF*7%7$Fe\\p$\"+bX7eJF*7$Fj\\p$\"+fQC*y$F*7$F_]p$ \"+ORhbOF*7%7$Fe]p$\"+FQ@eJF*7$Fj]p$\"+(ea\"*y$F*7$F_^p$\"+o+5cOF*7%7$ Fe^p$\"+*Hn$eJF*7$Fj^p$\"+:6+*y$F*7$F__p$\"+*G#ycOF*7%7$$!+y>al&*Feo$ \"+0_meJF*7$$!+Ek#=Q*Feo$\"+4Kq)y$F*7$$!+.ou\\(*Feo$\"+Yu!yl$F*7%7$$!+ J'4!ppFeo$\"+:pOfJF*7$$!+x3?:nFeo$\"+*\\,!)y$F*7$$!+Hfc(4(Feo$\"+#Q7&f OF*7%7$Feap$\"+V#Q<;$F*7$Fjap$\"+r,j&y$F*7$F_bp$\"+NM$Gm$F*7%7$$!+ikN) 3#Feo$\"+Y6_#=$F*7$$!+a#Q&p5Feo$\"+os%[w$F*7$F_cp$\"+6XLpOF*7%7$$\"+5o !R^$Ffs$\"+9)*)3u$F*7$$\"+*\\sQv\"Feo$\"+,'yk?$F*7$F_dp$\"+xkDkLF*7%7$ $\"+M/<^MFeo$\"+e8[%y$F*7$$\"+U1D;(*y$F*7 $Fjjn$\"+:,\"3U%F*7$F_[o$\"+&onsG%F*7%7$Fe[o$\"+Y$p)*y$F*7$Fj[o$\"+ipl ?WF*7$F_\\o$\"+7#Q!)G%F*7%7$Fe\\o$\"+J4B!z$F*7$Fj\\o$\"+x`H?WF*7$$!+w) H'=rFeo$\"+bkM*G%F*7%7$$!+7C$zN%Feo$\"+#eh9z$F*7$$!++-7jSFeo$\"+EZ1>WF *7$$!+ab#QX%Feo$\"+E!H?H%F*7%7$$!+M8xd>Feo$\"+YY%G!QF*7$$!+#QB,?\"Feo$ \"+i;o2WF*7$$!+a#y\"z;Feo$\"+Y+Y*H%F*7%7$$\"+NKF<^Ffs$\"+xb8$R%F*7$$\" +de`$f\"Feo$\"+J2RN_QFeo$\"+eE1#z$F*7$$\"+7^z0TFeo$\"+P4xPRF*7%7$Feao$\"+ kW;?WF*7$Fjao$\"+W=O!z$F*7$F_bo$\"+>]jKRF*7%7$Febo$\"+W\"41U%F*7$Fjbo$ \"+kr\"**y$F*7$$\"+ZzP:$*Feo$\"+A&[1$RF*7%7$Feco$\"+'f(y?WF*7$Fjco$\"+ 7(Q(*y$F*7$F_do$\"+%f)fHRF*7%7$Fedo$\"+$fw3U%F*7$Fjdo$\"+;(\\'*y$F*7$F _eo$\"+G+&*GRF*7%7$Feeo$\"+ws#4U%F*7$Fjeo$\"+K!*f*y$F*7$F_fo$\"+A)4&GR F*7%7$Fefo$\"+^)e4U%F*7$Fjfo$\"+duc*y$F*7$F_go$\"+U:>GRF*7%7$Fego$\"+V )z4U%F*7$Fjgo$\"+lka*y$F*7$F_ho$\"+C2&z#RF*7%7$Feho$\"+,X*4U%F*7$Fjho$ \"+2=`*y$F*7$F_io$\"+t@wFRF*7%7$Feio$\"+S^+@WF*7$Fjio$\"+p6_*y$F*7$F_j o$\"+X0hFRF*7%7$Fejo$\"+/J,@WF*7$Fjjo$\"+/K^*y$F*7$F_[p$\"+lf[FRF*7%7$ Fecm$\"+&z-6U%F*7$Fjcm$\"+29e_]F*7$F_dm$\"+h%ps\"\\F*7%7$Fedm$\"+X\">6 U%F*7$Fjdm$\"+e]c_]F*7$F_em$\"+ RD0&F*7$F_fm$\"+Oyu<\\F*7%7$Fefm$\"+9&*=@WF*7$Fjfm$\"+)o%\\_]F*7$F_gm$ \"+#QP\"=\\F*7%7$$!+g!pJ_*Feo$\"+KgF@WF*7$$!+W$*>C%*Feo$\"+q\"3C0&F*7$ $!+r:Mu(*Feo$\"+XJt=\\F*7%7$Fehm$\"+90[@WF*7$Fjhm$\"+)o.A0&F*7$F_im$\" +,lv>\\F*7%7$$!+E([:K%Feo$\"+k(y@U%F*7$Fjim$\"+Qa]^]F*7$F_jm$\"+iN\"># \\F*7%7$Fejm$\"+\"Q3)GWF*7$Fjjm$\"+@e([/&F*7$F_[n$\"+NE))G\\F*7%7$$\"+ :&*40jFfs$\"+4)Rf.&F*7$$\"+HKvu9Feo$\"+$RWxV%F*7$$\"+6$HNg\"Feo$\"+)z% e#f%F*7%7$$\"+9eYdNFeo$\"+.J;^]F*7$Fj\\n$\"+*4@DU%F*7$$\"+(*3\\$3%Feo$ \"+p2BmXF*7%7$Fe]n$\"+z&H@0&F*7$Fj]n$\"+BYb@WF*7$F_^n$\"+6y_iXF*7%7$Fe ^n$\"+Y6Q_]F*7$Fj^n$\"+cII@WF*7$F__n$\"+X*y5c%F*7%7$Fe_n$\"+q>[_]F*7$F j_n$\"+KA?@WF*7$F_`n$\"+H\"3.c%F*7%7$Fe`n$\"+DA`_]F*7$Fj`n$\"+x>:@WF*7 $F_an$\"+$)*H)fXF*7%7$Fean$\"+P3c_]F*7$Fjan$\"+lL7@WF*7$F_bn$\"+5X]fXF *7%7$Febn$\"+f'yD0&F*7$Fjbn$\"+Vb5@WF*7$F_cn$\"+'oo#fXF*7%7$Fecn$\"+10 f_]F*7$Fjcn$\"+'p$4@WF*7$F_dn$\"+p**3fXF*7%7$Fedn$\"+y()f_]F*7$Fjdn$\" +Ca3@WF*7$F_en$\"+h)\\*eXF*7%7$Feen$\"+\"y/E0&F*7$Fjen$\"+@%z5U%F*7$F_ fn$\"+vq$)eXF*7%7$Fefn$\"+v#4E0&F*7$Fjfn$\"+F\\2@WF*7$F_gn$\"+IVueXF*7 %7$Fe_l$\"+')>m_]F*7$Fj_l$\"+5,=%o&F*7$F_`l$\"+_![&[bF*7%7$Fe`l$\"+)*= n_]F*7$Fj`l$\"+)>qTo&F*7$F_al$\"+(R3([bF*7%7$Feal$\"+\"e(o_]F*7$Fjal$ \"+:X:%o&F*7$F_bl$\"+:Z#*[bF*7%7$Febl$\"+nXr_]F*7$Fjbl$\"+Hv7%o&F*7$F_ cl$\"+yCB\\bF*7%7$Fecl$\"+Xqw_]F*7$Fjcl$\"+^]2%o&F*7$F_dl$\"+z]q\\bF*7 %7$Fedl$\"+R6*G0&F*7$Fjdl$\"+d4&Ro&F*7$F_el$\"+wF_]bF*7%7$Feel$\"+0cJ` ]F*7$Fjel$\"+\"\\ENo&F*7$F_fl$\"+(GvAb&F*7%7$Fefl$\"+f8Sd]F*7$Fjfl$\"+ P2WzcF*7$$!+%*4vtrrFfs$\"+c&F*7%7$Feil$\"+ff!Ro&F*7$Fjil$\"+Ph$H0&F*7$F_jl$\"+$e6I>&F*7 %7$Fejl$\"+d'eSo&F*7$Fjjl$\"+RMy_]F*7$$\"+(p\"H*H*Feo$\"+Rm!>>&F*7%7$F e[m$\"+;)>To&F*7$Fj[m$\"+!GAF0&F*7$F_\\m$\"+UfJ\">&F*7%7$Fe\\m$\"+\"H] To&F*7$Fj\\m$\"+0=p_]F*7$F_]m$\"+E%[4>&F*7%7$Fe]m$\"+Rw;%o&F*7$Fj]m$\" +dWn_]F*7$F_^m$\"+Zxp!>&F*7%7$Fe^m$\"+W%yTo&F*7$Fj^m$\"+_Om_]F*7$F__m$ \"+[e^!>&F*7%7$Fe_m$\"+Ec=%o&F*7$Fj_m$\"+qkl_]F*7$F_`m$\"+UyP!>&F*7%7$ Fe`m$\"+T1>%o&F*7$Fj`m$\"+b9l_]F*7$F_am$\"+b&p->&F*7%7$Feam$\"+!G%>%o& F*7$Fjam$\"+;yk_]F*7$F_bm$\"+BB=!>&F*7%7$Febm$\"+/q>%o&F*7$Fjbm$\"+#4X E0&F*7$F_cm$\"+\\06!>&F*7%7$F($\"+8+B%o&F*7$F.$\"+x*pdJ'F*7$F3$\"+.Z\" *zhF*7%7$F9$\"+mjB%o&F*7$F>$\"+COw:jF*7$FC$\"+!)R/!='F*7%7$FI$\"+=kC%o &F*7$FN$\"+sNv:jF*7$FS$\"+/'=-='F*7%7$FY$\"+=PE%o&F*7$Fhn$\"+sit:jF*7$ F]o$\"+&[n/='F*7%7$Fco$\"+itH%o&F*7$Fio$\"+GEq:jF*7$F^p$\"+@2&3='F*7%7 $Fdp$\"+ZpP%o&F*7$Fip$\"+WIi:jF*7$F^q$\"+1q^\"='F*7%7$Fdq$\"+>%\\Yo&F* 7$Fiq$\"+r0N:jF*7$F^r$\"+U1'H='F*7%7$Fdr$\"+%Q#H(o&F*7$Fir$\"+1wq7jF*7 $F^s$\"+9RI)='F*7%7$$\"+5HW3yFfs$\"+V#z*3jF*7$Fjs$\"+Z2-\"p&F*7$F_t$\" +C*>6%eF*7%7$Fet$\"+zl@:jF*7$Fjt$\"+6My%o&F*7$F_u$\"+i%Hg#eF*7%7$$\"+? =_piFeo$\"+xTf:jF*7$$\"+_r0ijFeo$\"+8eS%o&F*7$$\"+0mwqmFeo$\"+i\"QQ#eF *7%7$Fev$\"+:@p:jF*7$Fjv$\"+vyI%o&F*7$$\"+xwt%H*Feo$\"+`n'H#eF*7%7$Few $\"+F8t:jF*7$Fjw$\"+j'oUo&F*7$F_x$\"+8#*\\AeF*7%7$Fex$\"+k3v:jF*7$Fjx$ \"+E\"\\Uo&F*7$F_y$\"+!o2A#eF*7%7$Fey$\"+%)>w:jF*7$Fjy$\"+1!QUo&F*7$F_ z$\"+M&3?#eF*7%7$Fez$\"+5*odJ'F*7$Fjz$\"+!3JUo&F*7$F_[l$\"+tQ'=#eF*7%7 $Fe[l$\"+8Nx:jF*7$Fj[l$\"+xkA%o&F*7$F_\\l$\"+KSv@eF*7%7$Fe\\l$\"+Fnx:j F*7$Fj\\l$\"+jKA%o&F*7$F_]l$\"+!zn;#eF*7%7$Fe]l$\"+g!zdJ'F*7$Fj]l$\"+J 4A%o&F*7$F_^l$\"+\"G)f@eF*7%7$Fe^l$\"+13y:jF*7$Fj^l$\"+%=>Uo&F*7$F__l$ \"+l5a@eF*-%&COLORG6&%$RGBG$\"\"(!\"\"$\"#&)!\"#$\"#vF^e`l-%+AXESLABEL SG6$%\"xG%%y(x)G-%%VIEWG6$;$!++++]AF*$\"++++]KF*;$!+++++mF*$\"+++++mF* " 2 364 364 364 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 436 -8952 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "soln_curve1 := plot(subs(_C=1,rhs(s oln)),x=-2..3,color=magenta):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "soln_curve2 := plot(subs(_C=-2,rhs(soln)),x=-2..3,color=navy):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "display(\{direction_field _plot,soln_curve1,soln_curve2\});" }}{PARA 13 "" 1 "" {INLPLOT "6'-%'C URVESG6]dl7%7$$!+)*=Y,?!\"*$!+#)*pdJ'F*7$$!+-\"Q&)*>F*$!+=+B%o&F*7$$!+ HQ1K?F*$!+#H&3?eF*7%7$$!+pa_QeF*7%7$$!+6\"ocZ\"F*$!+xNv:jF*7$$!+4.qr9F*$!+BkC%o&F *7$$!+h.X0:F*$!+#R\"y>eF*7%7$$!+n8%H@\"F*$!+xit:jF*7$$!+j7637F*$!+BPE% o&F*7$$!+2i/U7F*$!+5D`>eF*7%7$$!+7*RX]*!#5$!+LEq:jF*7$$!+#\\GGW*Feo$!+ ntH%o&F*7$$!+;j/&y*Feo$!+u#\\\">eF*7%7$$!+vx\"[)oFeo$!+[Ii:jF*7$$!+LFR *z'Feo$!+_pP%o&F*7$$!+1=mYrFeo$!+!*H[=eF*7%7$$!+MU()zUFeo$!+w0N:jF*7$$ !+y$y69%Feo$!+C%\\Yo&F*7$$!+&4(p*\\%Feo$!+`$Rq\"eF*7%7$$!+z_Ki/;\"F* $!+L8t:jF*7$$\"+T\\@#>\"F*$!+$y+v<'F*7%7$$\"+r_**=9F*$!+J\"\\Uo&F*7$$ \"+&**4JU\"F*$!+p3v:jF*7$$\"+Z)4^X\"F*$!+:BzxhF*7%7$$\"+oXZ#o\"F*$!+6! QUo&F*7$$\"+)[Yfo\"F*$!+*)>w:jF*7$$\"+pm3=q'e%> F*$!+&3JUo&F*7$$\"+F)p)[>F*$!+:*odJ'F*7$$\"+&H76)>F*$!+Ah8yhF*7%7$$\"+ MO?4AF*$!+#[EUo&F*7$$\"+-!\\=@#F*$!+=Nx:jF*7$$\"+Q$pTC#F*$!+jfCyhF*7%7 $$\"+GA]sCF*$!+oKA%o&F*7$$\"+)>m[Z#F*$!+Knx:jF*7$$\"+$zZs]#F*$!+0ALyhF *7%7$$\"+nPxNFF*$!+O4A%o&F*7$$\"+\\/\"zt#F*$!+k!zdJ'F*7$$\"+'\\T.x#F*$ !+9Uo&F*7$$\"+NY(4+$F*$!+63y:jF*7$$\"+TkWL IF*$!+I*e%yhF*7%7$$!+Xg#=+#F*$!+:,=%o&F*7$$!+bR<)*>F*$!+\"*>m_]F*7$$!+ Di&=.#F*$!+\\SH)=&F*7%7$$!+dZ%*Qn_]F* 7$$!+l/aoZ^V*Feo $!+\\qw_]F*7$$!+h/k!y*Feo$!+Aq8(=&F*7%7$$!+7KW&*oFeo$!+i4&Ro&F*7$$!+'H n()y'Feo$!+W6*G0&F*7$$!+)HS09(Feo$!+D$>j=&F*7%7$$!+!*Q3(H%Feo$!+'\\ENo &F*7$$!+A(oR7%Feo$!+5cJ`]F*7$$!+#4%o*[%Feo$!+9oc%=&F*7%7$$!+'pun!=Feo$ !+U2WzcF*7$$!+?+7^8Feo$!+k8Sd]F*7$$!+$*4vt2%y^F*7%7$$\"+$H&>r rFfs$!+W.2j]F*7$$\"+^O9)Q\"Feo$!+i\"z#oSFeo$!+l @.TbF*7%7$$\"+R\\,eiFeo$!+Uh$H0&F*7$$\"+LSctjFeo$!+kf!Ro&F*7$$\"+OqTo&F*7$$\"+2!oD>\"F*$!+fh_XbF*7%7$$\"+()G[=9F*$!+5=p_]F*7$$\"+zBiB 9F*$!+'H]To&F*7$$\"+4\")Rb9F*$!+wO*ea&F*7%7$$\"+&=U?o\"F*$!+iWn_]F*7$$ \"+r)yjo\"F*$!+Ww;%o&F*7$$\"+@-L=F*$!+dOm_] F*7$$\"+5QC\\>F*$!+\\%yTo&F*7$$\"+RJK\")>F*$!+`iKYbF*7%7$$\"+`T()3AF*$ !+vkl_]F*7$$\"+$[y@@#F*$!+Jc=%o&F*7$$\"+=_NWAF*$!+fUYYbF*7%7$$\"+(y2AZ #F*$!+g9l_]F*7$$\"+R1;vCF*$!+Y1>%o&F*7$$\"+%*RT2DF*$!+YDdYbF*7%7$$\"+J w]NFF*$!+@yk_]F*7$$\"+&ew\"QFF*$!+&G%>%o&F*7$$\"+%y\"\\qFF*$!+y(fma&F* 7%7$$\"+vDy)*HF*$!+(4XE0&F*7$$\"+Ju@,IF*$!+4q>%o&F*7$$\"+)f$eLIF*$!+_: tYbF*7%7$$!+1`M-?F*$!+79e_]F*7$$!+%paw*>F*$!++G5@WF*7$$!+_(f:.#F*$!+YZ TcXF*7%7$$!+@EaR6U%F*7$$!+b()>oRD0&F*7$$!+?<]q9F*$!+:]9@WF*7$$!+#*[w/: F*$!+rj$fb%F*7%7$$!+0,S97F*$!+$p%\\_]F*7$$!+DDl17F*$!+>&*=@WF*7$$!+./@ T7F*$!+DoabXF*7%7$$!+f!pJ_*Feo$!+v\"3C0&F*7$$!+X$*>C%*Feo$!+PgF@WF*7$$ !+s:Mu(*Feo$!+i5&\\b%F*7%7$$!+^$y0\"pFeo$!+$p.A0&F*7$$!+d@jtnFeo$!+>0[ @WF*7$$!+JNyJrFeo$!+1x#Rb%F*7%7$$!+D([:K%Feo$!+Va]^]F*7$$!+()Q]*4%Feo$ !+p(y@U%F*7$$!+9BNvWFeo$!+Y1x^XF*7%7$$!+%[p(o=Feo$!+Ee([/&F*7$$!+K_7*G \"Feo$!+'Q3)GWF*7$$!+_.\\Nx\\*))Feo$!+hII@WF*7$$\"+y'f(***)Feo$!+^6Q_]F*7$$\"+4,w0 $*Feo$!+i_g7\\F*7%7$$\"+I]%Q:\"F*$!+PA?@WF*7$$\"+YW%>;\"F*$!+v>[_]F*7$ $\"+C+2$>\"F*$!+ygP8\\F*7%7$$\"+YBv<9F*$!+#)>:@WF*7$$\"+?HNC9F*$!+IA`_ ]F*7$$\"+U#3eX\"F*$!+CU&Q\"\\F*7%7$$\"+ecU\"o\"F*$!+qL7@WF*7$$\"+)R&*p o\"F*$!+U3c_]F*7$$\"+#)on=F*$!+[b5@WF*7 $$\"+&4x(\\>F*$!+k'yD0&F*7$$\"+MLi\")>F*$!+@bT9\\F*7%7$$\"+8VS3AF*$!+, P4@WF*7$$\"+B$[E@#F*$!+60f_]F*7$$\"+F*>YC#F*$!+QUf9\\F*7%7$$\"+/zyrCF* $!+Ha3@WF*7$$\"+A0evCF*$!+$y)f_]F*7$$\"+;2l2DF*$!+YVt9\\F*7%7$$\"+.\"G ^t#F*$!+E%z5U%F*7$$\"+8hbQFF*$!+'y/E0&F*7$$\"+teqqFF*$!+Kr%[\"\\F*7%7$ $\"+FjV)*HF*$!+K\\2@WF*7$$\"+zOc,IF*$!+!G4E0&F*7$$\"+-!zP.$F*$!+y)R\\ \"\\F*7%7$$!+m?7.?F*$!+DP'4U%F*7$$!+Mz(o*>F*$!+$fi&*y$F*7$$!+/`6J?F*$! +3;(*y$F*7$ $!+\"es/C\"F*$!+G'eK#RF*7%7$$!+X/`R&*Feo$!+npl?WF*7$$!+fz$yS*Feo$!+_$p )*y$F*7$$!+Na)[w*Feo$!+-\")[ARF*7%7$$!+^CWF*7$$!+, -7jSFeo$!+(eh9z$F*7$$!+bb#QX%Feo$!+(G(\\=RF*7%7$$!+L8xd>Feo$!+n;o2WF*7 $$!+$QB,?\"Feo$!+^Y%G!QF*7$$!+b#y\"z;Feo$!+oi16RF*7%7$$\"+YKF<^Ffs$!+O 2RN_QFeo$!+bOY=WF*7$$\"+6^z0TFeo$!+w`vsUF*7%7$$ \"+`V<YS9kFeo$!+pW;?WF*7$$\"+7_s*p'Feo$!+%H\"* yF%F*7%7$$\"+`%fw())Feo$!+pr\"**y$F*7$$\"+:u2\"F*$!+>x#4G%F*7%7$$\"+F)fmT\"F*$!+@(\\'*y$F*7$$\"+RaW D9F*$!+)fw3U%F*7$$\"+)p>kX\"F*$!+'Gw:G%F*7%7$$\"+-N]!o\"F*$!+Q!*f*y$F* 7$$\"+av\"zo\"F*$!+\"GF4U%F*7$$\"+WS>>F*$ !+iuc*y$F*7$$\"+?[d]>F*$!+c)e4U%F*7$$\"+y82#)>F*$!+rZL#G%F*7%7$$\"+Z9q 2AF*$!+qka*y$F*7$$\"+*=^L@#F*$!+[)z4U%F*7$$\"+R^,XAF*$!+*evDG%F*7%7$$ \"+V(f6Z#F*$!+7=`*y$F*7$$\"+$o3iZ#F*$!+1X*4U%F*7$$\"+PU+3DF*$!+STw#G%F *7%7$$\"+*HgXt#F*$!+t6_*y$F*7$$\"+F*$!+1\"o!eJF*7$$!+^\\ SI?F*$!+Y#=@H$F*7%7$$!+G6'=u\"F*$!+kQC*y$F*7$$!+#3B=t\"F*$!+gX7eJF*7$$ !+!=now\"F*$!+%[a.:F*$!+^$o7H$F*7%7$$!+$)>s<7F*$!+?6+*y$F*7$$!+Z1L.7F*$!+/tOeJ F*7$$!+u>HR7F*$!+Ihe!H$F*7%7$$!+x>al&*Feo$!+9Kq)y$F*7$$!+Fk#=Q*Feo$!+5 _meJF*7$$!+/ou\\(*Feo$!+t4c*G$F*7%7$$!+I'4!ppFeo$!+/:+)y$F*7$$!+y3?:nF eo$!+@pOfJF*7$$!+Ifc(4(Feo$!+Qg&yG$F*7%7$$!+?,>:WFeo$!+w,j&y$F*7$$!+# \\ie+%Feo$!+[#Q<;$F*7$$!+O#G%>WFeo$!+%)\\`%G$F*7%7$$!+hkN)3#Feo$!+ts%[ w$F*7$$!+b#Q&p5Feo$!+^6_#=$F*7$$!+APT$f\"Feo$!+4R.yKF*7%7$$\"+Bo!R^$Ff s$!+0'yk?$F*7$$\"+)\\sQv\"Feo$!+>)*)3u$F*7$$\"+_acG6$e$F*7%7$ $\"+N/<^MFeo$!+iq)G;$F*7$$\"+T1Df j$F*7%7$$\"+A1UyhFeo$!+;/ifJF*7$$\"+]$eJX'Feo$!+3![xy$F*7$$\"+vc#3s'Fe o$!+jA^VOF*7%7$$\"+^f8]))Feo$!+Q\"e(eJF*7$$\"+<4gW!*Feo$!+'G5')y$F*7$$ \"+6gaI$*Feo$!+Z$4kk$F*7%7$$\"+SIP]6F*$!+L6TeJF*7$$\"+OkTl6F*$!+\"Hd*) y$F*7$$\"+\"R+]>\"F*$!+Dq#zk$F*7%7$$\"+u/#\\T\"F*$!+nyBeJF*7$$\"+#z%=F 9F*$!+d08*y$F*7$$\"+$[)Qd9F*$!+))*e)[OF*7%7$$\"+**[.z;F*$!+J\"R\"eJF*7 $$\"+dhQ*o\"F*$!+$HH#*y$F*7$$\"+BV,?F*$! +'fx!eJF*7$$\"+:b%=&>F*$!+G3H*y$F*7$$\"+mDy#)>F*$!+**G%*\\OF*7%7$$\"+, #\\$*>F*$!+tAqEDF*7$$!+Q Y;H?F*$!+%4r$fEF*7%7$$!+]HLW\"F*$!+EuOFDF*7$ $!+0\"GsB\"F*$!+-`@dEF*7%7$$!+')Q\\5'*Feo$!+?J=cJF*7$$!+=X(oL*Feo$!+5u -GDF*7$$!+\"GzKs*Feo$!+I&=el#F*7%7$$!+_=gIqFeo$!+;vjaJF*7$$!+c'3Ol'Feo $!+9IdHDF*7$$!+1XygqFeo$!+`Of`EF*7%7$$!+lK!=^%Feo$!+v_]\\JF*7$$!+Z$\\# 4RFeo$!+b_qMDF*7$$!+TW\"*fVFeo$!+Ynt\\EF*7%7$$!+B&=\"yAFeo$!+&4B'4JF*7 $$!+E>w(z)Ffs$!+NueuDF*7$$!+&f!>h9Feo$!+$yv%[EF*7%7$$\"+]m()4:Ffs$!+/J 67EF*7$$\"+:bFa>Feo$!+Eu4sIF*7$$\"+5uU.=Feo$!+k#4%=HF*7%7$$\"+.UiULFeo $!+@F9PDF*7$$\"+tozDSFeo$!+4y1ZJF*7$$\"+o\\b&>%Feo$!+u*>X*HF*7%7$$\"+d w%>6'Feo$!+,$G,`#F*7$$\"+:8j>lFeo$!+HA3aJF*7$$\"+=7McnFeo$!+J\"F* $!+TVx8IF*7%7$$\"+uW!>T\"F*$!+e*zq_#F*7$$\"+#z+-V\"F*$!+s08dJF*7$$\"+f Y0f9F*$!+<p\"F*$!+\\,NdJF* 7$$\"+D!G9s\"F*$!+F1@;IF*7%7$$\"+%=&oS>F*$!+0MsEDF*7$$\"+i;0a>F*$!+Dr[ dJF*7$$\"+7+,%)>F*$!+IG\"p,$F*7%7$$\"+,qj/AF*$!+oAjEDF*7$$\"+NcT;AF*$! +i#yv:$F*7$$\"+cssYAF*$!+d3WkdJF*7$$\"+cr`4DF*$!+QA&y,$F*7%7$$\"+&p$3KFF*$!+eB_EDF*7$$\"+@ 0gTFF*$!+s\")odJF*7$$\"+(G8Cx#F*$!+<<==IF*7%7$$\"+=&ec*HF*$!+Ox[EDF*7$ $\"+)[TV+$F*$!+%zAx:$F*7$$\"+'RQ`.$F*$!+/:X=IF*7%7$$!+n]t5?F*$!+LIEDDF *7$$!+L\\E*)>F*$!+.'*y&*=F*7$$!+G%)pE?F*$!+eNjD?F*7%7$$!+3.>\\\"F*$!+Xfe(*=F*7$$!+na7L7F*$!+>@^A?F*7%7 $$!+E-v(p*Feo$!+eLq@DF*7$$!+y\"='\\#*Feo$!+y#\\$**=F*7$$!+iVyq'*Feo$!+ F*[1-#F*7%7$$!+;`I[rFeo$!+2gk0f`'Feo$!+HmS.>F*7$$!+^+T))pFe o$!+_8-=?F*7%7$$!+$*)oto%Feo$!+>#\\[]#F*7$$!+>PoLPFeo$!+F*7$$!+r* [nC%Feo$!+;%Q],#F*7%7$$!+tV/EDFeo$!+#eV(HCF*7$$!+FM]=jFfs$!+a!48*>F*7$ $!+(p1.F\"Feo$!+$42%H?F*7%7$$!).]8aFeo$!+YJuR?F*7$$\"+$=)Rf@Feo$!+!\\4 8Q#F*7$$\"+GL0e=Feo$!+7A&4C#F*7%7$$\"+uG))\\JFeo$!+6t%>#>F*7$$\"+-#Q&= UFeo$!+D`5*\\#F*7$$\"+p1x(G%Feo$!+!H(3UBF*7%7$$\"+D7i&)fFeo$!+!GS[!>F* 7$$\"+Zx&fk'Feo$!+cB@;DF*7$$\"+_OT@oFeo$!+Bj.kBF*7%7$$\"+iv`5()Feo$!+k U*)**=F*7$$\"+1$*>%=*Feo$!+t$e6_#F*7$$\"+(eB_S*Feo$!+&*3WsBF*7%7$$\"+b NZR6F*$!+Sp%y*=F*7$$\"+@fJw6F*$!+'p0K_#F*7$$\"+$354?\"F*$!+W)enP#F*7%7 $$\"+)4$*fS\"F*$!+%)>\"o*=F*7$$\"+o@6O9F*$!+_1CCDF*7$$\"+v(pAY\"F*$!+R EOzBF*7%7$$\"+-+[r;F*$!+k$=i*=F*7$$\"+a5%pp\"F*$!+sU$[_#F*7$$\"+')*oTs \"F*$!+?m4\"Q#F*7%7$$\"+G_MO>F*$!+up%e*=F*7$$\"+=;Re>F*$!+ic?DDF*7$$\" +LvR')>F*$!+#fJBQ#F*7%7$$\"+px!3?#F*$!+3%*f&*=F*7$$\"+n[C?AF*$!+GKXDDF *7$$\"+)\\T)[AF*$!+YZD$Q#F*7%7$$\"+wZ*\\Y#F*$!+9iU&*=F*7$$\"+]OP#[#F*$ !+AkiDDF*7$$\"+TRV6DF*$!+7/(RQ#F*7%7$$\"+c])*GFF*$!+a.I&*=F*7$$\"+g\"* pWFF*$!+#G_d_#F*7$$\"+&*H8uFF*$!+07a%Q#F*7%7$$\"+A+$G*HF*$!+Rg?&*=F*7$ $\"+%)*pr+$F*$!+(fYe_#F*7$$\"+`6\"p.$F*$!+Bp+&Q#F*7%7$$!+AX%3-#F*$!+!3 \\2*=F*7$$!+ya:z>F*$!+ic9n7F*7$$!+l2m??F*$!+]Il*Q\"F*7%7$$!+,tug%)=F*7$$!+C:\"o<\"F*$!+l/qt7F*7$$!+5q?B7F*$!+ytk&Q\"F *7%7$$!+Ve!e*)*Feo$!+z]/y=F*7$$!+hDc^!*Feo$!+j'\\)z7F*7$$!+1n!fa*Feo$! +ra.%Q\"F*7%7$$!+\"p13S(Feo$!+O_&['=F*7$$!+LQ\"F*7%7$$!+:#)33]Feo$!+\\86I=F*7$$!+(RkHT$Feo$!+$R$y F8F*7$$!+yz%*>SFeo$!+roo)Q\"F*7%7$$!+VObfFFeo$!+G(o$=Feo$!+@w^![\"F*7$$\"+z; (GI#Feo$!+@rPx;F*7$$\"+IG.k=Feo$!+%QT(f:F*7%7$$\"+1h,?GFeo$!+s#=3M\"F* 7$$\"+q\\S[XFeo$!+qk2<=F*7$$\"+[*[AU%Feo$!+!)=6i;F*7%7$$\"+7cy>dFeo$!+ *y6uH\"F*7$$\"+gLz6pFeo$!+aH[g=F*7$$\"+WB)p%pFeo$!+QU\"Gq\"F*7%7$$\"+T e<.&)Feo$!+ekp\"G\"F*7$$\"+F5c\"R*Feo$!+%G)>w=F*7$$\"+gj&)3&*Feo$!+3L$ 3s\"F*7%7$$\"+YXvA6F*$!+zyiu7F*7$$\"+I\\.$>\"F*$!+joE$)=F*7$$\"+G(=&47 F*$!+U&3/t\"F*7%7$$\"+@/2#R\"F*$!+^O\"4F\"F*7$$\"+X[.]9F*$!+\"4\")p)=F *7$$\"+D?dp9F*$!+^#4it\"F*7%7$$\"+!3%ef;F*$!+M\"Q(o7F*7$$\"+wp$)3c+u\"F*7%7$$\"+Q_(f#>F*$!+)yftE\"F*7$$\"+3; wo>F*$!+a\\`!*=F*7$$\"+F^&>*>F*$!+iwxU#F*$!+qMVm7F*7$ $\"+C(G%HAF*$!+s7Y\"*=F*7$$\"+tsz`AF*$!+StzW:s#F*$! +gjIl7F*7$$\"+*\\k@v#F*$!+#Q)e#*=F*7$$\"+[1?yFF*$!+1WeZF*$!+(o'G*e'Feo7$$!+'=w'**>F*$!+-')) o^(Feo7%7$$!+4&>pz\"F*$!+4%>$G7F*7$$!+,Zww;F*$!+'QuTm'Feo7$$!+2Z/Kje09F*$!+H2hrnFeo7$$!+q,Aj9F*$ !+Kb0LvFeo7%7$$!+%GW&)G\"F*$!+Pwl,7F*7$$!+Y$3D8\"F*$!+-@zIpFeo7$$!+x&z F>\"F*$!+%)))yjvFeo7%7$$!+8G`P5F*$!+%egt<\"F*7$$!+t-/s&)Feo$!+PEwtrFeo 7$$!+9(Q??*Feo$!+Y:nGwFeo7%7$$!+m7&e)yFeo$!+WElR6F*7$$!+U#f$)z&Feo$!+N ?%3b(Feo7$$!+'e51X'Feo$!+D&4sv(Feo7%7$$!+7$e-S&Feo$!+/vC#3\"F*7$$!++Vz ?IFeo$!+LM*[7)Feo7$$!+8CYwOFeo$!+zx4&*zFeo7%7$$!+,mcuGFeo$!+9(\\C+\"F* 7$$!*:\"GLGFeo$!+K8(G#*)Feo7$$!+![Ss,*Ffs$!+q(3SQ)Feo7%7$$!*tx2a#Feo$! +HCL.\"*Feo7$$\"+`4MfBFeo$!+Vg.W)*Feo7$$\"+9v4K=Feo$!+*QV'**))Feo7%7$$ \"+\\\")>oCFeo$!+HEUn#)Feo7$$\"+FHA+\\Feo$!+%e%*z1\"F*7$$\"+ojK*\\%Feo $!+4=,G%*Feo7%7$$\"+(*o=U_Feo$!+\"o!)zk(Feo7$$\"+v?R*Q(Feo$!+z(Q*H6F*7 $$\"+rfo9rFeo$!+2Mnk)*Feo7%7$$\"+;ls=!)Feo$!+k_\\OsFeo7$$\"+_.,w)*Feo$ !+@t3r6F*7$$\"+Cr$pq*Feo$!+#o&\\=5F*7%7$$\"+a\"F*7$$\"++(o%H7F*$!+&>*3T5F*7%7$$\"+h&)[\"F*$!+nt4d5F*7%7$$\"+5;mA;F*$ !+>7e#o'Feo7$$\"+Y%fdu\"F*$!+D(ykA\"F*7$$\"+s>=[J@+#F*$!+8;#F*$!+&RH\\a'Feo7$$\"+uMtfAF*$!+3RCS7F*7$$\"+8S$*oAF *$!+53!R3\"F*7%7$$\"+>!z!HCF*$!++$zF]'Feo7$$\"+2%*G=DF*$!+<*eWC\"F*7$$ \"+=<#*HDF*$!+V=0*3\"F*7%7$$\"+')\\4'p#F*$!+Qq-rkFeo7$$\"+I#*exFF*$!+V TjZ7F*7$$\"+))GA\"z#F*$!+**p;$4\"F*7%7$$\"+RX_iHF*$!+8-eYkFeo7$$\"+oaZ PIF*$!+E)y+D\"F*7$$\"+\\/y_IF*$!+)4;l4\"F*7%7$$!+06nF@F*$!+[%*z@RFeo7$ $!+&*)GB(=F*$!+w+*RR#Feo7$$!+Y%pb$>F*$!+xQue>Feo7%7$$!+'eTa'=F*$!+-'4h #QFeo7$$!+CEC3;F*$!+B*z'*[#Feo7$$!+/%))3n\"F*$!+\\&Gu+#Feo7%7$$!+&p(4. ;F*$!+9PXGPFeo7$$!+D2FW8F*$!+5eL(e#Feo7$$!+IaDEMFeo7$$!+Sb2JbFeo$!+0T`*)GFeo7$$!+%HA n7'Feo$!+])>\">AFeo7%7$$!+vr]CbFeo$!+E:TBLFeo7$$!+Paa'*GFeo$!+)*zP#*HF eo7$$!+trv#[$Feo$!+Q.mvAFeo7%7$$!+Y?[%*GFeo$!+Yp.?KFeo7$$!*qETj#Feo$!+ yDv&4$Feo7$$!+N/H&R)Ffs$!+?,MLBFeo7%7$$!*FY/j#Feo$!+\"=ik6$Feo7$$\"+2y IoBFeo$!+VtK*>$Feo7$$\"+)=>H!=Feo$!+z2)>R#Feo7%7$$\"+Yk!)pBFeo$!+X4-8I Feo7$$\"+IYh)*\\Feo$!+z&oFI$Feo7$$\"+&)>bWWFeo$!+@RR^CFeo7%7$$\"+>*eS+ &Feo$!+1[/5HFeo7$$\"+`+_FwFeo$!+=Zu0MFeo7$$\"+g%Q6DFeo7%7 $$\"+TsoRwFeo$!+=z&y!GFeo7$$\"+j\\]D5F*$!+1;$z]$Feo7$$\"+N#p_s*Feo$!+ \"\\_#)H\"= F*$!+h#Gn!QFeo7$$\"+66)Rw\"F*$!+*4XJv#Feo7%7$$\"+dG]>=F*$!+>*fHT#Feo7$ $\"+*)RBv?F*$!+0'HG!RFeo7$$\"+8jiF?F*$!+i*pI\"GFeo7%7$$\"+a]n$3#F*$!+L 3+>BFeo7$$\"+$extL#F*$!+\"p)y'*RFeo7$$\"+`y=\"H#F*$!+x$HC(GFeo7%7$$\"+ Es%zM#F*$!+7(ytA#Feo7$$\"+,7U*f#F*$!+83T)3%Feo7$$\"+k$oYb#F*$!+>O1JHFe o7%7$$\"+\\2J7EF*$!+l!f#Q@Feo7$$\"+nMPhGF*$!+f/`xTFeo7$$\"+752=GF*$!+' 4F)))HFeo7%7$$\"+dnvwGF*$!+x!y<0#Feo7$$\"+\\KCBJF*$!+Z9,kUFeo7$$\"+2%* R\"3$F*$!+(R*eXIFeo7%7$$!+16nF@F*$\"+[+*RR#Feo7$Fj_v$\"+w$*z@RFeo7$F_` v$\"+(eXqN%Feo7%7$Fe`v$\"+$*)z'*[#Feo7$Fj`v$\"+J&4h#QFeo7$F_av$\"+:4O3 VFeo7%7$Feav$\"+ydL(e#Feo7$Fjav$\"+YOXGPFeo7$F_bv$\"+#HvyD%Feo7%7$Febv $\"+)>8no#Feo7$Fjbv$\"+Ei2HOFeo7$F_cv$\"+\"*[o0UFeo7%7$Fecv$\"+:%Feo7%7$Fedv$\"+kS `*)GFeo7$Fjdv$\"+g`DEMFeo7$$!+$HAn7'Feo$\"+>'pm4%Feo7%7$Feev$\"+`zP#*H Feo7$Fjev$\"+r9TBLFeo7$F_fv$\"+L\"H,/%Feo7%7$Fefv$\"+IDv&4$Feo7$Fjfv$ \"+%*o.?KFeo7$F_gv$\"+`$\\C)RFeo7%7$Fegv$\"+\"HF$*>$Feo7$Fjgv$\"+L@Y;J Feo7$$\"+(=>H!=Feo$\"+'p3Q#RFeo7%7$Fehv$\"+D&oFI$Feo7$Fjhv$\"+**3-8IFe o7$F_iv$\"+bbRkQFeo7%7$Feiv$\"+gYu0MFeo7$Fjiv$\"+kZ/5HFeo7$$\"+fx1FFeo7$$\"+dBVO7F *$\"+Q.\\$o$Feo7%7$Fe\\w$\"+4wq3PFeo7$Fj\\w$\"+:=32EFeo7$$\"+K-D+:F*$ \"+TB'Hi$Feo7%7$Fe]w$\"+\">Gn!QFeo7$$\"+)>#)H\"=F*$\"+L714DFeo7$$\"+76 )Rw\"F*$\"+)QWEc$Feo7%7$Fe^w$\"+L&HG!RFeo7$Fj^w$\"+\"*)fHT#Feo7$F__w$ \"+D&>F]$Feo7%7$$\"+`]n$3#F*$\"+<')y'*RFeo7$Fj_w$\"+33+>BFeo7$$\"+_y= \"H#F*$\"+8,OVMFeo7%7$$\"+Ds%zM#F*$\"+O2T)3%Feo7$Fj`w$\"+)oytA#Feo7$$ \"+j$oYb#F*$\"+tes%Q$Feo7%7$$\"+[2J7EF*$\"+\"QIv<%Feo7$$\"+oMPhGF*$\"+ V!f#Q@Feo7$F_bw$\"+(RipK$Feo7%7$Febw$\"+n8,kUFeo7$Fjbw$\"+d!y<0#Feo7$$ \"+1%*R\"3$F*$\"+(4+-F$Feo7%7$$!+WJc`?F*$\"+UmG*e'Feo7$$!+coVY>F*$\"+t \"3eB\"F*7$$!+&=w'**>F*$\"+#)z/V6F*7%7$Fe\\u$\"+UV $G7F*7$$!+3Z/K%3b(Feo7$$!+Q#f$)z&Fe o$\"+PElR6F*7$$!+#e51X'Feo$\"+*)e,>6F*7%7$$!+:$e-S&Feo$\"+&R$*[7)Feo7$ $!+(H%z?IFeo$\"+)\\ZA3\"F*7$$!+5CYwOFeo$\"+kqA&4\"F*7%7$Febu$\"+)GrG#* )Feo7$Fjbu$\"+3(\\C+\"F*7$$!+v/CoCFeo$\"+yX*z1\"F*7$$\"+HHA+\\Feo$\"+!fAuE)Feo7$F_eu$\"+&*Feo7 %7$$\"+%*o=U_Feo$\"+t(Q*H6F*7$$\"+y?R*Q(Feo$\"+W1)zk(Feo7$F_fu$\"+B]p# 3*Feo7%7$$\"+6ls=!)Feo$\"+:t3r6F*7$$\"+d.,w)*Feo$\"+E_\\OsFeo7$$\"+Dr$ pq*Feo$\"+;;Ti()Feo7%7$$\"+`\"F*7$$\"+Bx:Q7F*$\"+J2OrpF eo7$F_hu$\"+![wk`)Feo7%7$Fehu$\"+\\i)[@\"F*7$Fjhu$\"+$)e])z'Feo7$F_iu$ \"+oZRw$)Feo7%7$$\"+4;mA;F*$\"+?(ykA\"F*7$$\"+Z%fdu\"F*$\"+v6e#o'Feo7$ $\"+t>=[%)=F*7$F_[t$\"+ ftCsSFeo$\"+ly?pdFeo$\"+[H[g= F*7$$\"+iLz6pFeo$\"+%y6uH\"F*7$F_bt$\"++03b9F*7%7$$\"+Re<.&)Feo$\"+y#) >w=F*7$$\"+H5c\"R*Feo$\"+akp\"G\"F*7$F_ct$\"+I91P9F*7%7$Fect$\"+eoE$)= F*7$Fjct$\"+uyiu7F*7$F_dt$\"+&>'[F9F*7%7$Fedt$\"+'3\")p)=F*7$Fjdt$\"+Y O\"4F\"F*7$F_et$\"+([&o@9F*7%7$$\"+zSef;F*$\"+.m:*)=F*7$$\"+xp$)3F*$\"+\\\\`!*=F*7$ $\"+4;wo>F*$\"+$yftE\"F*7$$\"+G^&>*>F*$\"+wq6:9F*7%7$Fegt$\"+n7Y\"*=F* 7$Fjgt$\"+lMVm7F*7$F_ht$\"+(R(489F*7%7$Feht$\"+GH6#*=F*7$Fjht$\"+/=yl7 F*7$F_it$\"+6Da69F*7%7$Feit$\"+x$)e#*=F*7$Fjit$\"+bjIl7F*7$F_jt$\"+J.J 59F*7%7$Fejt$\"+4d%H*=F*7$Fjjt$\"+B!\\\\E\"F*7$F_[u$\"+U3J49F*7%7$$!+o ]t5?F*$\"+)f*y&*=F*7$Fjcr$\"+GIEDDF*7$F_dr$\"+t!>aR#F*7%7$Fedr$\"+:08' *=F*7$Fjdr$\"+6@#\\_#F*7$F_er$\"+fO>'R#F*7%7$Feer$\"+Mxm'*=F*7$Fjer$\" +#*[QCDF*7$$!+5/9)\\\"F*$\"+jr>(R#F*7%7$Fefr$\"+Sfe(*=F*7$Fjfr$\"+'omM _#F*7$F_gr$\"+70a)R#F*7%7$$!+F-v(p*Feo$\"+t#\\$**=F*7$$!+x\"='\\#*Feo$ \"+`Lq@DF*7$F_hr$\"+/PS+CF*7%7$$!+<`I[rFeo$\"+CmS.>F*7$$!+\">0f`'Feo$ \"+-gkF*7$$!+F*7$$!+ .M]=jFfs$\"+xNuHCF*7$$!+&p1.F\"Feo$\"+Qbk\"R#F*7%7$$!)/]8aFeo$\"+%[48Q #F*7$$\"+%=)Rf@Feo$\"+UJuR?F*7$F_\\s$\"+?/5!=#F*7%7$$\"+sG))\\JFeo$\"+ ?`5*\\#F*7$$\"+/#Q&=UFeo$\"+1t%>#>F*7$$\"+q1x(G%Feo$\"+T`'*y?F*7%7$$\" +C7i&)fFeo$\"+]B@;DF*7$$\"+[x&fk'Feo$\"+w-%[!>F*7$F_^s$\"+4j,d?F*7%7$$ \"+hv`5()Feo$\"+o$e6_#F*7$$\"+2$*>%=*Feo$\"+eU*)**=F*7$$\"+)eB_S*Feo$ \"+O\"o*=F*7$$\"+u(pAY\"F*$\"+#***oT?F*7%7$Fea s$\"+nU$[_#F*7$Fjas$\"+f$=i*=F*7$F_bs$\"+6g&*R?F*7%7$Febs$\"+dc?DDF*7$ Fjbs$\"+pp%e*=F*7$F_cs$\"+R5sQ?F*7%7$Fecs$\"+BKXDDF*7$Fjcs$\"+.%*f&*=F *7$F_ds$\"+&)yzP?F*7%7$Feds$\"+A3P ?F*7%7$Fees$\"+xAvDDF*7$Fjes$\"+\\.I&*=F*7$F_fs$\"+E9^O?F*7%7$Fefs$\"+ #fYe_#F*7$Fjfs$\"+Ng?&*=F*7$F_gs$\"+5d/O?F*7%7$Fe_q$\"+oAqEDF*7$Fj_q$ \"+_#3v:$F*7$F_`q$\"+J%R[-$F*7%7$Fe`q$\"+]z#o_#F*7$Fj`q$\"+qDQdJF*7$F_ aq$\"+(*zNDIF*7%7$Feaq$\"+Dl-FDF*7$Fjaq$\"+&*R=dJF*7$F_bq$\"+iY/EIF*7% 7$Febq$\"+@uOFDF*7$Fjbq$\"+*4Vo:$F*7$F_cq$\"+B_*p-$F*7%7$Fecq$\"+0u-GD F*7$Fjcq$\"+:J=cJF*7$F_dq$\"+'*>RGIF*7%7$$!+`=gIqFeo$\"+4IdHDF*7$$!+b' 3Ol'Feo$\"+6vjaJF*7$$!+0XygqFeo$\"+sohIIF*7%7$$!+mK!=^%Feo$\"+]_qMDF*7 $$!+Y$\\#4RFeo$\"+q_]\\JF*7$$!+SW\"*fVFeo$\"+zPZMIF*7%7$$!+D&=\"yAFeo$ \"+IueuDF*7$$!+7>w(z)Ffs$\"+!4B'4JF*7$$!+$f!>h9Feo$\"+UZtNIF*7%7$$\"+M m()4:Ffs$\"+?u4sIF*7$$\"+Feo$\"++J67EF*7$$\"+6uU.=Feo$\"+i7!ew#F* 7%7$$\"+-UiULFeo$\"+/y1ZJF*7$$\"+uozDSFeo$\"+;F9PDF*7$F_iq$\"+^0p*o#F* 7%7$$\"+cw%>6'Feo$\"+CA3aJF*7$$\"+;8j>lFeo$\"+'HG,`#F*7$F_jq$\"+%z[un# F*7%7$Fejq$\"+4x(f:$F*7$Fjjq$\"+6GBGDF*7$F_[r$\"+B$HGn#F*7%7$Fe[r$\"+c eucJF*7$Fj[r$\"+kYYFDF*7$F_\\r$\"+%=O/n#F*7%7$Fe\\r$\"+n08dJF*7$Fj\\r$ \"+`*zq_#F*7$F_]r$\"+3)y*oEF*7%7$Fe]r$\"+W,NdJF*7$Fj]r$\"+w.'o_#F*7$F_ ^r$\"+**)**zm#F*7%7$Fe^r$\"+?r[dJF*7$Fj^r$\"++MsEDF*7$F__r$\"+&p(HnEF* 7%7$Fe_r$\"+d#yv:$F*7$Fj_r$\"+jAjEDF*7$F_`r$\"+o'pnm#F*7%7$Fe`r$\"+M>k dJF*7$Fj`r$\"+'eol_#F*7$F_ar$\"+)Gejm#F*7%7$Fear$\"+n\")odJF*7$Fjar$\" +aB_EDF*7$F_br$\"+4)Ggm#F*7%7$Febr$\"+*yAx:$F*7$Fjbr$\"+Jx[EDF*7$F_cr$ \"+@!fdm#F*7%7$Fe[p$\"+,\"o!eJF*7$Fj[p$\"+8.I*y$F*7$F_\\p$\"+t,DbOF*7% 7$Fe\\p$\"+bX7eJF*7$Fj\\p$\"+fQC*y$F*7$F_]p$\"+ORhbOF*7%7$Fe]p$\"+FQ@e JF*7$Fj]p$\"+(ea\"*y$F*7$F_^p$\"+o+5cOF*7%7$Fe^p$\"+*Hn$eJF*7$Fj^p$\"+ :6+*y$F*7$F__p$\"+*G#ycOF*7%7$$!+y>al&*Feo$\"+0_meJF*7$$!+Ek#=Q*Feo$\" +4Kq)y$F*7$$!+.ou\\(*Feo$\"+Yu!yl$F*7%7$$!+J'4!ppFeo$\"+:pOfJF*7$$!+x3 ?:nFeo$\"+*\\,!)y$F*7$$!+Hfc(4(Feo$\"+#Q7&fOF*7%7$Feap$\"+V#Q<;$F*7$Fj ap$\"+r,j&y$F*7$F_bp$\"+NM$Gm$F*7%7$$!+ikN)3#Feo$\"+Y6_#=$F*7$$!+a#Q&p 5Feo$\"+os%[w$F*7$F_cp$\"+6XLpOF*7%7$$\"+5o!R^$Ffs$\"+9)*)3u$F*7$$\"+* \\sQv\"Feo$\"+,'yk?$F*7$F_dp$\"+xkDkLF*7%7$$\"+M/<^MFeo$\"+e8[%y$F*7$$ \"+U1D;(*y$F*7$Fjjn$\"+:,\"3U%F*7$F_[o$ \"+&onsG%F*7%7$Fe[o$\"+Y$p)*y$F*7$Fj[o$\"+ipl?WF*7$F_\\o$\"+7#Q!)G%F*7 %7$Fe\\o$\"+J4B!z$F*7$Fj\\o$\"+x`H?WF*7$$!+w)H'=rFeo$\"+bkM*G%F*7%7$$! +7C$zN%Feo$\"+#eh9z$F*7$$!++-7jSFeo$\"+EZ1>WF*7$$!+ab#QX%Feo$\"+E!H?H% F*7%7$$!+M8xd>Feo$\"+YY%G!QF*7$$!+#QB,?\"Feo$\"+i;o2WF*7$$!+a#y\"z;Feo $\"+Y+Y*H%F*7%7$$\"+NKF<^Ffs$\"+xb8$R%F*7$$\"+de`$f\"Feo$\"+J2RN_QFeo$\"+ eE1#z$F*7$$\"+7^z0TFeo$\"+P4xPRF*7%7$Feao$\"+kW;?WF*7$Fjao$\"+W=O!z$F* 7$F_bo$\"+>]jKRF*7%7$Febo$\"+W\"41U%F*7$Fjbo$\"+kr\"**y$F*7$$\"+ZzP:$* Feo$\"+A&[1$RF*7%7$Feco$\"+'f(y?WF*7$Fjco$\"+7(Q(*y$F*7$F_do$\"+%f)fHR F*7%7$Fedo$\"+$fw3U%F*7$Fjdo$\"+;(\\'*y$F*7$F_eo$\"+G+&*GRF*7%7$Feeo$ \"+ws#4U%F*7$Fjeo$\"+K!*f*y$F*7$F_fo$\"+A)4&GRF*7%7$Fefo$\"+^)e4U%F*7$ Fjfo$\"+duc*y$F*7$F_go$\"+U:>GRF*7%7$Fego$\"+V)z4U%F*7$Fjgo$\"+lka*y$F *7$F_ho$\"+C2&z#RF*7%7$Feho$\"+,X*4U%F*7$Fjho$\"+2=`*y$F*7$F_io$\"+t@w FRF*7%7$Feio$\"+S^+@WF*7$Fjio$\"+p6_*y$F*7$F_jo$\"+X0hFRF*7%7$Fejo$\"+ /J,@WF*7$Fjjo$\"+/K^*y$F*7$F_[p$\"+lf[FRF*7%7$Fecm$\"+&z-6U%F*7$Fjcm$ \"+29e_]F*7$F_dm$\"+h%ps\"\\F*7%7$Fedm$\"+X\">6U%F*7$Fjdm$\"+e]c_]F*7$ F_em$\"+RD0&F*7$F_fm$\"+Oyu<\\F *7%7$Fefm$\"+9&*=@WF*7$Fjfm$\"+)o%\\_]F*7$F_gm$\"+#QP\"=\\F*7%7$$!+g!p J_*Feo$\"+KgF@WF*7$$!+W$*>C%*Feo$\"+q\"3C0&F*7$$!+r:Mu(*Feo$\"+XJt=\\F *7%7$Fehm$\"+90[@WF*7$Fjhm$\"+)o.A0&F*7$F_im$\"+,lv>\\F*7%7$$!+E([:K%F eo$\"+k(y@U%F*7$Fjim$\"+Qa]^]F*7$F_jm$\"+iN\">#\\F*7%7$Fejm$\"+\"Q3)GW F*7$Fjjm$\"+@e([/&F*7$F_[n$\"+NE))G\\F*7%7$$\"+:&*40jFfs$\"+4)Rf.&F*7$ $\"+HKvu9Feo$\"+$RWxV%F*7$$\"+6$HNg\"Feo$\"+)z%e#f%F*7%7$$\"+9eYdNFeo$ \"+.J;^]F*7$Fj\\n$\"+*4@DU%F*7$$\"+(*3\\$3%Feo$\"+p2BmXF*7%7$Fe]n$\"+z &H@0&F*7$Fj]n$\"+BYb@WF*7$F_^n$\"+6y_iXF*7%7$Fe^n$\"+Y6Q_]F*7$Fj^n$\"+ cII@WF*7$F__n$\"+X*y5c%F*7%7$Fe_n$\"+q>[_]F*7$Fj_n$\"+KA?@WF*7$F_`n$\" +H\"3.c%F*7%7$Fe`n$\"+DA`_]F*7$Fj`n$\"+x>:@WF*7$F_an$\"+$)*H)fXF*7%7$F ean$\"+P3c_]F*7$Fjan$\"+lL7@WF*7$F_bn$\"+5X]fXF*7%7$Febn$\"+f'yD0&F*7$ Fjbn$\"+Vb5@WF*7$F_cn$\"+'oo#fXF*7%7$Fecn$\"+10f_]F*7$Fjcn$\"+'p$4@WF* 7$F_dn$\"+p**3fXF*7%7$Fedn$\"+y()f_]F*7$Fjdn$\"+Ca3@WF*7$F_en$\"+h)\\* eXF*7%7$Feen$\"+\"y/E0&F*7$Fjen$\"+@%z5U%F*7$F_fn$\"+vq$)eXF*7%7$Fefn$ \"+v#4E0&F*7$Fjfn$\"+F\\2@WF*7$F_gn$\"+IVueXF*7%7$Fe_l$\"+')>m_]F*7$Fj _l$\"+5,=%o&F*7$F_`l$\"+_![&[bF*7%7$Fe`l$\"+)*=n_]F*7$Fj`l$\"+)>qTo&F* 7$F_al$\"+(R3([bF*7%7$Feal$\"+\"e(o_]F*7$Fjal$\"+:X:%o&F*7$F_bl$\"+:Z# *[bF*7%7$Febl$\"+nXr_]F*7$Fjbl$\"+Hv7%o&F*7$F_cl$\"+yCB\\bF*7%7$Fecl$ \"+Xqw_]F*7$Fjcl$\"+^]2%o&F*7$F_dl$\"+z]q\\bF*7%7$Fedl$\"+R6*G0&F*7$Fj dl$\"+d4&Ro&F*7$F_el$\"+wF_]bF*7%7$Feel$\"+0cJ`]F*7$Fjel$\"+\"\\ENo&F* 7$F_fl$\"+(GvAb&F*7%7$Fefl$\"+f8Sd]F*7$Fjfl$\"+P2WzcF*7$$!+%*4vtrrFfs$\"+c&F*7%7$Feil$ \"+ff!Ro&F*7$Fjil$\"+Ph$H0&F*7$F_jl$\"+$e6I>&F*7%7$Fejl$\"+d'eSo&F*7$F jjl$\"+RMy_]F*7$$\"+(p\"H*H*Feo$\"+Rm!>>&F*7%7$Fe[m$\"+;)>To&F*7$Fj[m$ \"+!GAF0&F*7$F_\\m$\"+UfJ\">&F*7%7$Fe\\m$\"+\"H]To&F*7$Fj\\m$\"+0=p_]F *7$F_]m$\"+E%[4>&F*7%7$Fe]m$\"+Rw;%o&F*7$Fj]m$\"+dWn_]F*7$F_^m$\"+Zxp! >&F*7%7$Fe^m$\"+W%yTo&F*7$Fj^m$\"+_Om_]F*7$F__m$\"+[e^!>&F*7%7$Fe_m$\" +Ec=%o&F*7$Fj_m$\"+qkl_]F*7$F_`m$\"+UyP!>&F*7%7$Fe`m$\"+T1>%o&F*7$Fj`m $\"+b9l_]F*7$F_am$\"+b&p->&F*7%7$Feam$\"+!G%>%o&F*7$Fjam$\"+;yk_]F*7$F _bm$\"+BB=!>&F*7%7$Febm$\"+/q>%o&F*7$Fjbm$\"+#4XE0&F*7$F_cm$\"+\\06!>& F*7%7$F($\"+8+B%o&F*7$F.$\"+x*pdJ'F*7$F3$\"+.Z\"*zhF*7%7$F9$\"+mjB%o&F *7$F>$\"+COw:jF*7$FC$\"+!)R/!='F*7%7$FI$\"+=kC%o&F*7$FN$\"+sNv:jF*7$FS $\"+/'=-='F*7%7$FY$\"+=PE%o&F*7$Fhn$\"+sit:jF*7$F]o$\"+&[n/='F*7%7$Fco $\"+itH%o&F*7$Fio$\"+GEq:jF*7$F^p$\"+@2&3='F*7%7$Fdp$\"+ZpP%o&F*7$Fip$ \"+WIi:jF*7$F^q$\"+1q^\"='F*7%7$Fdq$\"+>%\\Yo&F*7$Fiq$\"+r0N:jF*7$F^r$ \"+U1'H='F*7%7$Fdr$\"+%Q#H(o&F*7$Fir$\"+1wq7jF*7$F^s$\"+9RI)='F*7%7$$ \"+5HW3yFfs$\"+V#z*3jF*7$Fjs$\"+Z2-\"p&F*7$F_t$\"+C*>6%eF*7%7$Fet$\"+z l@:jF*7$Fjt$\"+6My%o&F*7$F_u$\"+i%Hg#eF*7%7$$\"+?=_piFeo$\"+xTf:jF*7$$ \"+_r0ijFeo$\"+8eS%o&F*7$$\"+0mwqmFeo$\"+i\"QQ#eF*7%7$Fev$\"+:@p:jF*7$ Fjv$\"+vyI%o&F*7$$\"+xwt%H*Feo$\"+`n'H#eF*7%7$Few$\"+F8t:jF*7$Fjw$\"+j 'oUo&F*7$F_x$\"+8#*\\AeF*7%7$Fex$\"+k3v:jF*7$Fjx$\"+E\"\\Uo&F*7$F_y$\" +!o2A#eF*7%7$Fey$\"+%)>w:jF*7$Fjy$\"+1!QUo&F*7$F_z$\"+M&3?#eF*7%7$Fez$ \"+5*odJ'F*7$Fjz$\"+!3JUo&F*7$F_[l$\"+tQ'=#eF*7%7$Fe[l$\"+8Nx:jF*7$Fj[ l$\"+xkA%o&F*7$F_\\l$\"+KSv@eF*7%7$Fe\\l$\"+Fnx:jF*7$Fj\\l$\"+jKA%o&F* 7$F_]l$\"+!zn;#eF*7%7$Fe]l$\"+g!zdJ'F*7$Fj]l$\"+J4A%o&F*7$F_^l$\"+\"G) f@eF*7%7$Fe^l$\"+13y:jF*7$Fj^l$\"+%=>Uo&F*7$F__l$\"+l5a@eF*-%&COLORG6& %$RGBG$\"\"(!\"\"$\"#&)!\"#$\"#vF^e`l-F$6$7_o7$$F^e`l\"\"!$\"1a\\I'))R m'>!#<7$$!1nm;HU,\"*=!#:$\"1JfYS;D![#Fie`l7$$!1L$3FH'='z\"F]f`l$\"1Bk+ x[uTIFie`l7$$!1nmTgBa*o\"F]f`l$\"1[Z8&Hft$QFie`l7$$!1nm\"H_\">#e\"F]f` l$\"1(*40N'zf'[Fie`l7$$!1L$3_!4Nv9F]f`l$\"1g0&oK?&*='Fie`l7$$!1n;/wfHw 8F]f`l$\"1x2!=4T2x(Fie`l7$$!1+]PM.tt7F]f`l$\"1eK(=_ds))*Fie`l7$$!1n;/, oln6F]f`l$\"13AHJ6%pF\"!#;7$$!1+](oWB>1\"F]f`l$\"1J7;)RH5m\"Fch`l7$$!1 KLLepjJ&*Fch`l$\"1J?,&z%[)>#Fch`l7$$!1lm;z/ot&)Fch`l$\"1%o!\\a%*eTGFch `l7$$!1*****\\P[_\\(Fch`l$\"1nceIu]TQFch`l7$$!1*****\\7)Q7kFch`l$\"1xt ]:sl!G&Fch`l7$$!1+++D;&)o`Fch`l$\"1E5j^Kg$H(Fch`l7$$!1L$3x1O]*[Fch`l$ \"1-Czx&e@\\)Fch`l7$$!1mmT50A@WFch`l$\"1NF`![D4#**Fch`l7$$!1**\\P%)z!y &QFch`l$\"1'G`3*[O)>\"F]f`l7$$!1KLLeaR%H$Fch`l$\"1RE@'f0DX\"F]f`l7$$!1 KL$e96r\"GFch`l$\"1!3w1B9?r\"F]f`l7$$!1KLLLo#)RBFch`l$\"1$H9:>sq,#F]f` l7$$!1*\\PMFHA1#Fch`l$\"1h#e0\"HW;AF]f`l7$$!1m;a8y^LF]f`l7$$!1SLLL3`lCFie`l$\"1@n> W)\\Tz$F]f`l7$$\"1YLe9TOEHFie`l$\"1(p/&=ab=UF]f`l7$$\"1L+]i!f#=$)Fie`l $\"1pn.D:X9XF]f`l7$$\"1.]PfQa)3\"Fch`l$\"1!y$4kur%f%F]f`l7$$\"1.+]7=EX 8Fch`l$\"1'*R:HX$>j%F]f`l7$$\"1-D1*y?OZ\"Fch`l$\"1&H6Y\\ZVj%F]f`l7$$\" 1-]il(z>g\"Fch`l$\"1.ZZ0TBEYF]f`l7$$\"1-v=U(Q.t\"Fch`l$\"1DgS5'ozg%F]f `l7$$\"1-+v=xpe=Fch`l$\"1=Z;6\\/!e%F]f`l7$$\"1P$eRA9WR#Fch`l$\"1-[#3nT PP%F]f`l7$$\"1rm;H28IHFch`l$\"1Wex\"*p9kSF]f`l7$$\"1p;a8d3AMFch`l$\"1O Bm9pcNPF]f`l7$$\"1om\"zpSS\"RFch`l$\"1-@l].u)R$F]f`l7$$\"1+]P41oWWFch` l$\"1^=V*\\(o]IF]f`l7$$\"1LL$3_?`(\\Fch`l$\"1:8t\"pcAt#F]f`l7$$\"1M$3_ D1l_&Fch`l$\"1K*3lg1&QCF]f`l7$$\"1OLe*)>pxgFch`l$\"1T\\;7NV#=#F]f`l7$$ \"1omm\"z+vb'Fch`l$\"1YS(op5z)>F]f`l7$$\"1,+v$f4t.(Fch`l$\"1X<6q>*p\"= F]f`l7$$\"1PL$e*Gst!)Fch`l$\"1#*[)or^^^\"F]f`l7$$\"1+++]#RW9*Fch`l$\"1 fnw)o]$y7F]f`l7$$\"1++DJE>>5F]f`l$\"1t0*)zj2+6F]f`l7$$\"1+]i!RU07\"F]f `l$\"1c'=%z[uT'*Fch`l7$$\"1++v=S2L7F]f`l$\"13T\\x:AU%)Fch`l7$$\"1mmm\" p)=M8F]f`l$\"1*fwc(>/svFch`l7$$\"1++](=]@W\"F]f`l$\"1[IJ)y*z1oFch`l7$$ \"1L$e*[$z*R:F]f`l$\"1GFz!y?pA'Fch`l7$$\"1,+]iC$pk\"F]f`l$\"1'*G([\"=( )*o&Fch`l7$$\"1m;H2qcZp[Fch`l7$$\"1mm;/Ogb>F]f`l$\"1=7QOeRQXFch`l7$$\"1+]ilAFj?F]f`l$ \"1et/;#4aB%Fch`l7$$\"1MLL$)*pp;#F]f`l$\"13FaPSSyRFch`l7$$\"1ML3xe,tAF ]f`l$\"1:@\\X<8XPFch`l7$$\"1n;HdO=yBF]f`l$\"1'p\\SOI(QNFch`l7$$\"1,++D >#[Z#F]f`l$\"19!*pydxnLFch`l7$$\"1nmT&G!e&e#F]f`l$\"1.tx&=h2>$Fch`l7$$ \"1MLL$)Qk%o#F]f`l$\"1!*>S#Rss/$Fch`l7$$\"1+]iSjE!z#F]f`l$\"14]5\\#yw! HFch`l7$$\"1,]P40O\"*GF]f`l$\"1%)\\Pr8U&y#Fch`l7$$\"\"$Ffe`l$\"1As!G;0 \\m#Fch`l-%'COLOURG6&Fhd`l$\"*++++\"!\")Ffe`lFijal-F$6$7dp7$Fee`l$!1Q$ 4T,lP&))!#=7$F[f`l$!1wS\"QGLT4\"Fie`l7$Faf`l$!1nwL**oK98Fie`l7$Fff`l$! 1V_gc*GOh\"Fie`l7$F[g`l$!15=$R/98)>Fie`l7$F`g`l$!1&G97u!3FCFie`l7$Feg` l$!1(3L0E5c#HFie`l7$Fjg`l$!1-peI?'[a$Fie`l7$F_h`l$!1hR?Fh];VFie`l7$Feh `l$!1*odMa3SC&Fie`l7$Fjh`l$!1(GktPH`R'Fie`l7$F_i`l$!11Rp,Vg1wFie`l7$Fd i`l$!1#R(\\yRLM#*Fie`l7$Fii`l$!1aV;v:q?6Fch`l7$F^j`l$!1R*GGer)\\8Fch`l 7$Fhj`l$!1#QTfu&f)f\"Fch`l7$Fb[al$!1i8wKNFch`l7$F\\\\al$!1'pieV#eGB Fch`l7$F`]al$!1-GPf([P'GFch`l7$Fj]al$!15r#H_7DY$Fch`l7$Fd^al$!1Z6Cy8w7 VFch`l7$Fb`al$!18))=mrj/aFch`l7$F\\aal$!1\"ej['\\pCqFch`l7$Ffaal$!1#3& e2u)QG*Fch`l7$F[bal$!1!4Al;#Q/6F]f`l7$F`bal$!1UfCY8rX8F]f`l7$Febal$!1. %34_TXr\"F]f`l7$Fjbal$!1DC!pv#yF F]f`l7$F_cal$!1?x\"o'\\ZwKF]f`l7$$\"1N$3F>0uz'Fch`l$!1`!*o5Iu)4%F]f`l7 $Fdcal$!15jV`5#oV&F]f`l7$$\"1HT'H(Fch`l$!1IJZ(4;&4$)F]f`l7$$\"1W5l]()=htFch`l$!1Lh#epQhb*F]f`l7$$ \"1`7.#ekfU(Fch`l$!1SwxG,JB6!#97$$\"1d8s(\\_$euFch`l$!1c(**pG>4B\"Fhbb l7$$\"1h9T8/u!\\(Fch`l$!1&>g!z+)4O\"Fhbbl7$$\"1l:5H$GJ_(Fch`l$!1Or&yfQ 8_\"Fhbbl7$$\"1p;zWi^bvFch`l$!1\\0o\"*)yRs\"Fhbbl7$$\"1t<[gT!ze(Fch`l$ !1CQd_^;))>Fhbbl7$$\"1x='=**zEl( Fch`l$!1WYThEFiGFhbbl7$$\"1'3_v!z1&o(Fch`l$!1Z(\\7\"))4lOFhbbl7$$\"1!> UK#eXCbD#!#87$$\"1.DJq&>Y\"yFch`l$\"1#GWea$ywJ F`fbl7$$\"13E+'[2q%yFch`l$\"1-CB1yiN$*Fhbbl7$$\"18Fp,aRzyFch`l$\"1VJ!R !>0xaFhbbl7$$\"1y#=2\")Fch`l$\"1))>\\R&o9T\"Fhbbl7$$\"1a(o zmU19)Fch`l$\"1GK?&>LQF\"Fhbbl7$$\"1ik.aD5u\")Fch`l$\"1.T)=4#*3;\"Fhbb l7$$\"1qT5SCc2#)Fch`l$\"1$eJb\"eam5Fhbbl7$$\"1(eRA@#[u#)Fch`l$\"1%Hnb! ojy\"*F]f`l7$$\"1.]P%)>ST$)Fch`l$\"1qn..Q3g!)F]f`l7$$\"1OekG:Cv%)Fch`l $\"1UX3.21*['F]f`l7$$\"1pm\"H2\"34')Fch`l$\"1\\'>%HwLQaF]f`l7$$\"1N$e9 ;gn())Fch`l$\"1^!zT6$)37%F]f`l7$F^dal$\"1_(fl=*)zK$F]f`l7$$\"1,+D\"y#= o'*Fch`l$\"1\"*H\"f6!=LCF]f`l7$Fcdal$\"1'z$H1EMH>F]f`l7$$\"1+v$4^n)p5F ]f`l$\"14\\4`%*Q9;F]f`l7$Fhdal$\"1\\hRP0^#R\"F]f`l7$F]eal$\"1U3b/N^v5F ]f`l7$Fbeal$\"1I!*\\l/L))*)Fch`l7$Fgeal$\"1:!f@06Qo(Fch`l7$F\\fal$\"13 ;_TBx6oFch`l7$Fafal$\"1kbMCdnugFch`l7$Fffal$\"1#fd5_WG_&Fch`l7$F[gal$ \"1$4@5i(f]]Fch`l7$F`gal$\"1)e\\\\.Wbm%Fch`l7$Fegal$\"1]yq3)ySK%Fch`l7 $Fjgal$\"1YNqp@nTSFch`l7$F_hal$\"1*30Q!=J!z$Fch`l7$Fdhal$\"1-ff#3C8d$F ch`l7$Fihal$\"1^MeU+1#R$Fch`l7$F^ial$\"1&zMU7)>3KFch`l7$Fcial$\"1\"\\F ZS-.1$Fch`l7$Fhial$\"1TJ+kLFqEFch`l-Fgjal6&Fhd`l$\")!\\DP\"F[[blFd`cl$\")viobF[[bl-%+AXE SLABELSG6$%\"xG%%y(x)G-%%VIEWG6$;$!++++]AF*$\"++++]KF*;$!+++++mF*$\"++ +++mF*" 2 607 362 362 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 442 8 "Code for" }{TEXT -1 1 " " }{TEXT 412 13 " Bernoulli_ode" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 494 115 "You must execute this function here in order to use it \+ later in the worksheet! You must also execute the function " }{TEXT 499 13 "separable_ode" }{TEXT 500 20 " in the subsection." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 10 " Code for " }{TEXT 498 14 " separable_ode" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3700 "separable_ode := proc()\noption `Copyright \2511997-2001 Brian E . Blank, All Rights Reserved.`:\nlocal xx, yy, x_0, y_0, expr, cc, LI ST1, LIST2, LIST3, NF1, NF2, NF3, jj, kk, yy_integrand, xx_integrand,x i,eta;\nglobal _C;\n\nif nargs < 1 or nargs > 2 then \nERROR(`separabl e_ode expects one or two arguments.`);\nfi:\n\nif nargs = 1 and not ty pe(args[1],equation) then\nERROR(`separable_ode expects its argument t o be an equation.`):\nelif nargs = 2 and (not type(args[1],equation) o r not type(args[2],equation))\nthen\nERROR(`separable_ode expects its \+ arguments to be equations.`):\nfi:\n\nif nargs = 2 then\nif (not type( lhs(args[2]),function) or not type(op(0,lhs(args[2])), name) or nops( lhs(args[2]) ) <> 1 or not type(rhs(args[2]),algebraic))\nthen ERROR( `\n\"separable_ode expects its second argument to be of the form y(a) \+ = c.`):\nelse \ny_0 := rhs(args[2]);\nx_0 := op(1,lhs(args[2])):\nyy : = op(0,lhs(args[2])):\nfi:\nfi:\n \n\nif not has(lhs(args[1]), diff) t hen\nERROR(`separable_ode expects its first argument to be of the form diff(y(x),x)=F(x,y(x)).`):\nelif nops(op(1,lhs(args[1]))) <> 1\nthen \nERROR(`separable_ode expects its first argument to be of the form di ff(y(x),x)=F(x,y(x)) where y(x) is a function of one variable.`):\neli f not type(op(1,(op(1,lhs(args[1])))),name)\nthen\nERROR(`separable_od e expects its first argument to be of the form diff(y(x),x)=F(x,y(x)) \+ where y(x) is a function of one variable and x is a name of a variable .`):\nelse\nxx := op(1,(op(1,lhs(args[1])))):\nexpr := rhs(args[1]):\n fi;\n\n\nif not type(rhs(args[1]), algebraic) then\nERROR(`separable_o de expects its first argument to be of the form diff(y(x),x)=F(x,y(x)) .`):\nfi:\n\nif nargs = 2 and op(0,op(1,lhs(args[1])))<>yy\nthen\nERRO R(`separable_ode expects the dependent variable names in the first two arguments to be the same.`):\nfi:\n\nif nargs = 1 then yy := op(0,op( 1,lhs(args[1]))): fi:\n\nif type(factor(numer(expr)),`*`) then\n LI ST1 := [op(factor(numer(expr)))];\nelse\n LIST1 := [numer(expr)];\n fi;\nif type(denom(expr),`*`) then\n LIST2 := map(z->z^(-1),[op(fact or(denom(expr)))]);\nelse\n LIST2 := [denom(expr)^(-1)];\nfi;\nNF1 \+ := nops(LIST1);\nNF2 := nops(LIST2); \nLIST3 := [];\nfor kk from 1 to \+ NF1 do\nif type(LIST1[kk], `^`) and nops(op(1,LIST1[kk])) > 1 and type (op(1,LIST1[kk]),`*`) then\n for jj from 1 to nops(op(1,LIST1[kk])) \+ do\n LIST3 := [op(LIST3),op(jj,op(1,LIST1[kk]))^op(2,LIST1[kk])];\n \+ od;\nelse\nLIST3 := [op(LIST3),LIST1[kk]];\nfi;\nod; \n\nfor kk from 1 to NF2 do\nif type(LIST2[kk], `^`) and nops(op(1,LIST2[kk])) > 1 an d type(op(1,LIST2[kk]),`*`) then\n for jj from 1 to nops(op(1,LIST2[ kk])) do\n LIST3 := [op(LIST3),op(jj,op(1,LIST2[kk]))^(-op(2,LIST2[k k]))];\n od:\nelse\nLIST3 := [op(LIST3),LIST2[kk]];\nfi;\nod;\n\nNF3 := nops(LIST3);\n\nyy_integrand := 1;\nxx_integrand := 1;\n\nfor jj f rom 1 to NF3 do\nif has(LIST3[jj],yy(xx) ) \n then yy_integrand := y y_integrand*LIST3[jj]^(-1);\nelse\n xx_integrand := xx_integrand*LIS T3[jj];\nfi;\nod;\n\nNF3 := nops(LIST3);\n\nyy_integrand := 1;\nxx_int egrand := 1;\n\nfor jj from 1 to NF3 do\nif has(LIST3[jj],yy(xx) ) \n \+ then yy_integrand := yy_integrand*LIST3[jj]^(-1);\nelse\n xx_integ rand := xx_integrand*LIST3[jj];\nfi;\nod;\n\n\nyy_integrand := subs(yy (xx)=yy,yy_integrand);\nif has(yy_integrand,xx) then\nERROR(`The first argument of separable_ode does not appear to be a separable equation. `);\nfi:\n\nif nargs = 1\nthen\nRETURN( [args[1],\n Int(yy_inte grand,yy)=Int(xx_integrand,xx)+_C,\n subs(yy = yy(xx), \+ int(yy_integrand,yy))=int(xx_integrand,xx)+_C]);\n\nelse\nRETURN( [arg s[1],\nInt(subs(yy=eta,yy_integrand),eta=y_0..yy(xx))=Int(subs(xx=xi,x x_integrand),xi=x_0..xx),\nint(subs(yy=eta,yy_integrand),eta=y_0 ..yy( xx))=int(subs(xx=xi,xx_integrand),xi=x_0..xx)]);\nfi:\n\nend:" }}}} {PARA 0 "" 0 "" {TEXT -1 2 " \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9052 "Bernoulli_ode := proc()\noption `Copyright \2511997-2000 Bri an E. Blank, All Rights Reserved.`:\nlocal xx, yy, yy2, x_0, y_0, dif f_count, diff_indx, expr, aa_yy, deriv, aa, yy_lhs, eqn1, eqn2, Eqn3, \+ eqn3, eqn4, cc, LIST, LIST1, LIST2, LIST3, NF1, NF2, NF3, jj, kk, nn, \+ zz, oi, ff_xx, yy_rhs, eqtns;\n\nif nargs < 1 or nargs > 2 then \nERRO R(`Bernoulli_ode expects one or two arguments.`);\nfi:\n\nif nargs = 1 and not type(args[1],equation) then\nERROR(`Bernoulli_ode expects its argument to be an equation.`):\nelif nargs = 2 and (not type(args[1], equation) or not type(args[2],equation))\nthen\nERROR(`Bernoulli_ode e xpects its arguments to be equations.`):\nfi:\n\nif nargs = 2 then\nif (not type( lhs(args[2]),function) or not type(op(0,lhs(args[2])), nam e) or nops( lhs(args[2]) ) <> 1 or not type(rhs(args[2]),algebraic))\n then ERROR(`Bernoulli_ode expects its second argument to be of the for m y(a) = c.`):\nelse \ny_0 := rhs(args[2]);\nx_0 := op(1,lhs(args[2])) :\nyy2 := op(0,lhs(args[2])):\nfi:\nfi:\n\n########################### ########################\n# \+ #\n# The next section checks to see if the equation #\n# is of \+ the form diff(y(x),x) = f(x)*y(x)^n #\n# If so, separable_ode wi ll be called. # \n# \+ #\n###################################################\n\n## #### Begin Check for Separability Section #####\n\nif not type(lhs(arg s[1]),`+`) then\n\nif not has(lhs(args[1]), diff) then\nERROR(`Bernoul li_ode expects its first argument to be of the form diff(y(x),x)+a(x)* y(x)=f(x)*y(x)^n.`):\nelif nops(op(1,lhs(args[1]))) <> 1\nthen\nERROR( `Bernoulli_ode expects its first argument to be of the form diff(y(x), x)+a(x)*y(x)=f(x)*y(x)^n where y(x) is a function of one variable.`): \nelif not type(op(1,(op(1,lhs(args[1])))),name)\nthen\nERROR(`Bernoul li_ode expects its first argument to be of the form diff(y(x),x)+a(x)* y(x)=f(x)*y(x)^n where y(x) is a function of one variable and x is a n ame of a variable.`):\nelse\nxx := op(1,(op(1,lhs(args[1])))):\nexpr : = rhs(args[1]):\nfi;\n\n\nif not type(rhs(args[1]), algebraic) then\nE RROR(`Bernoulli_ode expects its first argument to be of the form diff( y(x),x)+a(x)*y(x)=f(x)*y(x)^n.`):\nfi:\n\nif nargs = 2 and op(0,op(1,l hs(args[1])))<>yy\nthen\nERROR(`Bernoulli_ode expects the dependent va riable names in the first two arguments to be the same.`):\nfi:\n\nif \+ nargs = 1 then\nprintf(`Switching to type [separable].\\nCalling separ able_ode:\\n\\n`):\nRETURN(separable_ode(args[1]));\nelse\nprintf(`Swi tching to type [separable].\\nCalling separable_ode:\\n\\n`):\nRETURN( separable_ode(args[1],args[2]));\nfi:\n\nfi: \n\n###### End Check for \+ Separability Section #####\n\n######### From here on, nops(lhs(args[1] )) > 1 #########\n\nif nops(lhs(args[1])) > 2 then\nERROR(`Bernoulli_o de expects the left side of its first argument to be of the form diff( y(x),x)+a(x)*y(x).`):\nfi:\n\n######################################## ###################\n# \+ #\n# The next section checks that diff appears exactly once \+ #\n# on the left. The index, 1 or 2, that it appears in is #\n# cal led diff_indx. #\n# \+ #\n# Maple will have arran ged a proper lhs #\n# so that diff_indx = 2 but it c an't hurt to be sure. #\n# \+ #\n################################################### ########\n\n############# Begin diff check #############\n\ndiff_count := 0:\nfor jj from 1 to 2 do\nif has(op(jj,lhs(args[1])),diff) then \+ \n diff_count := diff_count+1:\n diff_indx := jj:\nfi:\nod:\n\n\nif \+ diff_count <> 1 then\nERROR(`Bernoulli_ode expects the left side of it s first argument to be of the form diff(y(x),x)+a(x)*y(x).`):\nfi:\n\n \nif not has(op(diff_indx,lhs(args[1])),diff) then\nERROR(`Bernoulli_o de expects the left side of its first argument to be of the form diff( y(x),x)+a(x)*y(x).`):\nfi:\n############# End diff check ############# \n\noi := 3-diff_indx:\naa_yy := op(oi,lhs(args[1])):\nderiv := op(dif f_indx,lhs(args[1])):\n\n############# Begin finding variables ####### ######\n\nif nops(op(1,deriv)) <>1 or nops(op(2,deriv)) <> 1\nthen\nER ROR(`Bernoulli_ode expects the left side of its first argument to be o f the form diff(y(x),x)+a(x)*y(x).`):\nelif not type(op(1,op(1,deriv)) ,name)\nor\nnot type( op(2,deriv),name) then\nERROR(`Bernoulli_ode exp ects the left side of its first argument to be of the form diff(y(x),x )+a(x)*y(x).`):\n\nelse\nxx := op(1,op(1,deriv)):\nif xx<>op(2,deriv) \nthen\nERROR(`Bernoulli_ode expects the left side of its first argume nt to be of the form diff(y(x),x)+a(x)*y(x).`):\nfi:\nyy := op(0,op(1, deriv)):\nif nargs = 2 and yy2<>yy\nthen\nERROR(`Bernoulli_ode expects the dependent variable names in the first two arguments to be the sam e.`):\nfi:\nfi;\n\n\nif not type(rhs(args[1]), algebraic) then\nERROR( `Bernoulli_ode expects its first argument to be of the form diff(y(x), x)=F(x,y(x)).`):\nfi:\n############# End finding variables ########### ##\n\n\n\n\n###### Begin finding coeff of yy(xx) on lhs of ode ###### \n\nexpr := aa_yy:\nif type(factor(numer(expr)),`*`) then\n LIST1 : = [op(factor(numer(expr)))];\nelse\n LIST1 := [numer(expr)];\nfi;\n if type(denom(expr),`*`) then\n LIST2 := map(z->z^(-1),[op(factor(de nom(expr)))]);\nelse\n LIST2 := [denom(expr)^(-1)];\nfi;\nNF1 := no ps(LIST1);\nNF2 := nops(LIST2); \nLIST3 := [];\nfor kk from 1 to NF1 d o\nif type(LIST1[kk], `^`) and nops(op(1,LIST1[kk])) > 1 and type(op(1 ,LIST1[kk]),`*`) then\n for jj from 1 to nops(op(1,LIST1[kk])) do\n \+ LIST3 := [op(LIST3),op(jj,op(1,LIST1[kk]))^op(2,LIST1[kk])];\n od; \nelse\nLIST3 := [op(LIST3),LIST1[kk]];\nfi;\nod; \n\nfor kk from 1 to NF2 do\nif type(LIST2[kk], `^`) and nops(op(1,LIST2[kk])) > 1 and typ e(op(1,LIST2[kk]),`*`) then\n for jj from 1 to nops(op(1,LIST2[kk])) do\n LIST3 := [op(LIST3),op(jj,op(1,LIST2[kk]))^(-op(2,LIST2[kk]))] ;\n od:\nelse\nLIST3 := [op(LIST3),LIST2[kk]];\nfi;\nod;\n\nNF3 := n ops(LIST3);\n\naa := 1:\nyy_lhs := 1:\n\nfor jj from 1 to NF3 do\nif h as(LIST3[jj],yy(xx) ) \n then yy_lhs := yy_lhs*LIST3[jj];\nelse\n \+ aa := aa*LIST3[jj];\nfi;\nod;\n\n\n\n\nif yy_lhs <> yy(xx)\nthen\nERRO R(`Bernoulli_ode expects the left side of its first argument to be of \+ the type diff(y(x),x)+a(x)*y(x).`);\nfi:\n###### End finding coeff of \+ yy(xx) on lhs of ode ######\n\n\n############# Begin checking rhs of o de #############\nexpr := factor(rhs(args[1])):\n\nif type(factor(nume r(expr)),`*`) then\n LIST1 := [op(factor(numer(expr)))];\nelse\n \+ LIST1 := [numer(expr)];\nfi;\nif type(denom(expr),`*`) then\n LIST2 := map(z->z^(-1),[op(factor(denom(expr)))]);\nelse\n LIST2 := [den om(expr)^(-1)];\nfi;\nNF1 := nops(LIST1);\nNF2 := nops(LIST2); \nLIST3 := [];\nfor kk from 1 to NF1 do\nif type(LIST1[kk], `^`) and nops(op( 1,LIST1[kk])) > 1 and type(op(1,LIST1[kk]),`*`) then\n for jj from 1 to nops(op(1,LIST1[kk])) do\n LIST3 := [op(LIST3),op(jj,op(1,LIST1[ kk]))^op(2,LIST1[kk])];\n od;\nelse\nLIST3 := [op(LIST3),LIST1[kk]]; \nfi;\nod; \n\nfor kk from 1 to NF2 do\nif type(LIST2[kk], `^`) and no ps(op(1,LIST2[kk])) > 1 and type(op(1,LIST2[kk]),`*`) then\n for jj \+ from 1 to nops(op(1,LIST2[kk])) do\n LIST3 := [op(LIST3),op(jj,op(1, LIST2[kk]))^(-op(2,LIST2[kk]))];\n od:\nelse\nLIST3 := [op(LIST3),LI ST2[kk]];\nfi;\nod;\n\nNF3 := nops(LIST3);\n\nff_xx := 1:\nyy_rhs := 1 :\n\nfor jj from 1 to NF3 do\nif has(LIST3[jj],yy(xx) ) \n then yy_r hs := yy_rhs*LIST3[jj];\nelse\n ff_xx := ff_xx*LIST3[jj];\nfi;\nod; \n\n\n\nif has(ff_xx,yy) then\nERROR(`The first argument passed to Ber noulli_ode does not appear to be a differential equation of Bernoulli \+ type.`):\nfi:\n\nnn := simplify(log[2](subs(yy(xx)=2,yy_rhs))):\nif yy _rhs <> yy(xx)^nn then \nERROR(`The first argument passed to Bernoulli _ode does not appear to be a separable differential equation.`):\nfi: \n############# End checking rhs of ode #############\n\n\n\n\n\n\n\n# ##################################################\n# \+ #\n# The next section checks to see if the equation #\n# is of the form diff(y(x),x)+a(x)*y(x)=f(x)*y(x) # \n# If so, separable_ode(\{args\}) will be called. # \n# \+ #\n############################# ######################\n\n\n###### Begin Check for Separability Sectio n #####\n\nif nn = 1 then \nprintf(`Equation is separable. Switching \+ to type separable:\\n`);\nif nargs = 2 then\nRETURN( [args[1],op(separ able_ode(\{diff(yy(xx),xx)=(ff_xx-aa)*yy(xx),args[2]\}))]);\nelse\nRET URN([args[1],op(separable_ode(diff(yy(xx),xx)=(ff_xx-aa)*yy(xx)))]);\n fi: \nfi:\n###### End Check for linearity Section #####\n\nif nn = 0 t hen \nprintf(`Equation is linear. Switching to type linear:\\n`);\nRE TURN( linear_ode(args) ); \nfi:\n\n\n###### Now we are in true Bernoul li case #####\neqn1 := args[1]:\neqn2 := zeta(xx) = yy(xx)^(1-nn);\neq n3 := diff(zeta(xx),xx) + (1-nn)*aa*zeta(xx) = (1-nn)*ff_xx;\nif nargs = 2 then\nLIST := [eqn1, eqn2, op(linear_ode(eqn3, zeta(x_0)=y_0^(1-n n)))];\nelse\nLIST := [eqn1, eqn2, op(linear_ode(eqn3))];\n\nfi:\nLIST := [op(LIST), subs(zeta(xx)=yy(xx)^(1-nn),LIST[nops(LIST)]) ];\n\nRET URN(LIST);\nend:" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {MPLTEXT 0 21 1 "\n" }}{SECT 0 {PARA 4 "" 0 "" {TEXT 443 14 "Description of" }{TEXT -1 2 " " }{TEXT 444 13 "Bernoulli_ode" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 13 "Bernoulli_ode" }{TEXT 30 82 " - Exhibit steps for solving a first order differential equation of Bernoulli type" }}{PARA 4 "" 0 "usage" {TEXT -1 18 "Calling Sequences:" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 413 43 "Bernoulli_ode(ode)\n Bernoulli_ode(ode, ic) " }}{PARA 4 "" 0 "" {TEXT -1 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 23 72 "ode - an equation of the form diff(y(x), x) + a(x)*y(x) = f(x)*y(x)^n " }}{PARA 0 "" 0 "" {TEXT -1 5 " " } {TEXT 23 65 "ic - an equation of the form y(a) = c (the initial co ndition)" }}{PARA 0 "" 0 "" {TEXT 23 1 "\n" }{TEXT 414 12 "Description :" }}{PARA 15 "" 0 "" {TEXT -1 3 "If " }{TEXT 457 14 " Bernoulli_ode" }{TEXT -1 46 " is not used in a package, then the function " }{TEXT 458 13 "separable_ode" }{TEXT -1 36 " should be executed prior to usi ng " }{TEXT 456 13 "Bernoulli_ode" }{TEXT -1 57 ". (This requirement w ill only be noticed when a(x) = 0.)" }}{PARA 15 "" 0 "" {TEXT -1 9 "T he call " }{TEXT 415 52 " Bernoulli_ode(diff(y(x),x)+a(x)*y(x) = f(x)* y(x)^n)" }{TEXT -1 66 " returns (in general) a list with 10 entries. \+ The first entry is " }{TEXT 453 38 " diff(y(x),x)+a(x)*y(x) = f(x)*y(x )^n " }{TEXT -1 128 " and the last entry is the solution of this diffe rential equation (in implicit equation form). Further details will be \+ provided." }}{PARA 15 "" 0 "" {TEXT -1 67 "The required form of the eq uation passed as the first argument of " }{TEXT 427 13 "Bernoulli_ode " }{TEXT -1 80 " is strictly enforced. In particular, the left hand s ide of the first equation " }{TEXT 417 4 "must" }{TEXT -1 17 " be of t he form " }{TEXT 416 22 "diff(y(x),x)+a(x)*y(x)" }{TEXT -1 95 " and \+ nothing else, apart from the order of the terms. For example, the diff erential equations " }{TEXT 418 41 "\n diff(y(x),x)+ y(x)-y( x)^2 = 0" }{TEXT -1 2 ", " }{TEXT 419 34 " \n x*diff(y(x),x) =y(x)^3" }{TEXT -1 7 ", \nand " }{TEXT 420 38 "\n y(x)-diff( y(x),x) = y(x)^2" }{TEXT -1 145 ",\nwhile perfectly valid as different ial equations of Bernoulli type, nevertheless result in error messages when passed as the first argument of " }{TEXT 428 13 "Bernoulli_ode " }{TEXT -1 2 ". " }}{PARA 15 "" 0 "" {TEXT -1 4 "If " }{TEXT 421 1 " x" }{TEXT -1 6 " and " }{TEXT 422 2 " y" }{TEXT -1 108 " are respect ively the independent and dependent variables of the differential equa tion, then the expression" }{TEXT 424 2 "y " }{TEXT -1 73 "cannot appe ar on either the left or right side of the first argument of " } {TEXT 455 13 "Bernoulli_ode" }{TEXT -1 20 ". It must appear as " } {TEXT 423 4 "y(x)" }{TEXT -1 8 ". Thus, " }{TEXT 425 21 "diff(y(x),x) \+ = x/y(x)" }{TEXT -1 32 " is a valid first argument but " }{TEXT 426 19 " diff(y(x),x) = x/y" }{TEXT -1 9 " is not." }}{PARA 15 "" 0 "" {TEXT -1 9 "The call " }{TEXT 429 23 " Bernoulli_ode(diff_eq)" }{TEXT -1 33 " results in a check of type for " }{TEXT 454 7 "diff_eq" } {TEXT -1 49 ". If the Bernoulli type cannot be verified, then " } {TEXT 430 22 "Bernoulli_ode(diff_eq)" }{TEXT -1 36 " returns a string \+ with that message." }}{PARA 15 "" 0 "" {TEXT -1 40 "If the first order differential equation" }{TEXT 465 8 " diff_eq" }{TEXT -1 18 " is of \+ the form " }{TEXT 466 36 "diff(y(x),x)+a(x)*y(x) = f(x)*y(x)^n" } {TEXT -1 8 " with " }{TEXT 467 4 "n=0 " }{TEXT -1 4 "or " }{TEXT 468 3 "n=1" }{TEXT -1 23 ", then the return of " }{TEXT 469 22 "Bern oulli_ode(diff_eq)" }{TEXT -1 58 " is a list with two entries. The fi rst is the return of " }{TEXT 470 31 "dsolve(diff_eq,[linear],useInt) " }{TEXT -1 34 " and the second is the return of " }{TEXT 471 24 "dso lve(diff_eq,[linear])" }{TEXT -1 115 ". In other words, the integrals \+ are evaluated, if possible, in the second entry. If is called with tw o arguments, " }{TEXT 472 7 "diff_eq" }{TEXT -1 4 " and" }{TEXT 473 3 " ic" }{TEXT -1 23 ", then the returns are " }{TEXT 474 36 "dsolve(\{d iff_eq,ic\},[linear],useInt)" }{TEXT -1 6 " and " }{TEXT 475 29 "dsol ve(\{diff_eq,ic\},[linear])" }{TEXT -1 1 "." }}{PARA 15 "" 0 "" {TEXT -1 40 "If the first order differential equation" }{TEXT 476 8 " diff_e q" }{TEXT -1 18 " is of the form " }{TEXT 477 26 "diff(y(x),x) = f(x )*y(x)^n" }{TEXT -1 25 " , then the returns of " }{TEXT 478 22 "Bern oulli_ode(diff_eq)" }{TEXT -1 7 " and " }{TEXT 480 25 "Bernoulli_ode (diff_eq,ic)" }{TEXT -1 18 " include those of" }{TEXT 479 23 " separa ble_ode(diff_eq)" }{TEXT -1 6 " and " }{TEXT 481 25 "separable_ode(di ff_eq,ic)" }{TEXT -1 15 " respectively." }}{PARA 15 "" 0 "" {TEXT -1 40 "If the first order differential equation" }{TEXT 431 8 " diff_eq" }{TEXT -1 18 " is of the form " }{TEXT 460 36 "diff(y(x),x)+a(x)*y(x ) = f(x)*y(x)^n" }{TEXT -1 8 " with " }{TEXT 463 4 "n<>0" }{TEXT -1 6 " and " }{TEXT 464 4 "n<>1" }{TEXT -1 7 ", then " }{TEXT 459 22 "Be rnoulli_ode(diff_eq)" }{TEXT -1 46 " implements the change of variable \n\n " }{XPPEDIT 18 0 "y(x) = zeta(x)^(1/(1-n));" "/-%\"yG6#% \"xG)-%%zetaG6#F&*&\"\"\"F,,&F,F,%\"nG!\"\"F/" }{TEXT -1 56 ". \n\nThi s equation is the second entry of the return of " }{TEXT 461 22 "Bern oulli_ode(diff_eq)" }{TEXT -1 36 ". The third entry of the return of \+ " }{TEXT 433 22 "Bernoulli_ode(diff_eq)" }{TEXT -1 179 "is the differe ntial equation that results when the aforementioned change of variable is made (but prior to any further algebraic manipulation). The fourth entry of the return of " }{TEXT 434 23 "Bernoulli_ode(diff_eq) " } {TEXT -1 443 "is obtained by multiplying the third entry by an integra ting factor. The integrating factor is expressed as an unevaluated int egral. The fifth entry rewrites the left side of the equation as the d erivative of a product. In the sixth entry the derivative is removed b y integration. In the seventh entry the integrating factor is evaluate d, if possible. The eighth entry evaluates the remaining integral, if \+ possible. The ninth entry solves for " }{XPPEDIT 19 1 "zeta(x)" "-%%ze taG6#%\"xG" }{TEXT -1 101 ". In the tenth and last entry, a substituti on is made to convert the equation back to a function of " }{XPPEDIT 19 1 "y(x)" "-%\"yG6#%\"xG" }{TEXT -1 3 ". " }}{PARA 15 "" 0 "" {TEXT -1 21 "The final entry of " }{TEXT 435 22 "Bernoulli_ode(diff_ eq)" }{TEXT -1 48 " is an equation that provides the solution to " } {TEXT 436 3 "ode" }{TEXT -1 57 " in implicit form involving a constan t of integration, " }{TEXT 437 2 "_C" }{TEXT -1 19 ". If the call is " }{TEXT 438 29 "Bernoulli_ode(diff_eq,y(a)=c)" }{TEXT -1 50 ", then the constant of integration is solved for." }}{PARA 15 "" 0 "" {TEXT -1 116 "No attempt is made to verify the correctness of the solu tion. It is recommended that the user test for correctness. " }}{PARA 15 "" 0 "" {TEXT -1 17 "Because the name " }{XPPEDIT 19 1 "zeta" "I%ze taG6\"" }{TEXT -1 4 " (" }{TEXT 509 4 "zeta" }{TEXT -1 55 ") is use d as the change of variable, the arguments of " }{TEXT 439 14 " Bernou lli_ode" }{TEXT -1 20 " should be free of " }{TEXT 462 4 "zeta" } {TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 432 9 "Examples:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 440 14 "First example:" }{TEXT -1 2 "\n\n" }{TEXT 482 88 "W e will start by redoing the equation of Bernoulli type that we have co nsidered already:" }{TEXT -1 2 "\n\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "diff_eq := diff(y(x),x) - 2*y(x) = -3*x*y(x)^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%(diff_eqG/,&-%%diffG6$-%\"yG6#%\"xGF -\"\"\"F*!\"#,$*&F-F.F*\"\"#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Bernoulli_ode(diff_eq); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7,/,&-%%diffG6$-%\"yG6#%\"xGF,\"\"\"F)!\"#,$*&F,F-F)\" \"#!\"$/-%%zetaGF+*$F)!\"\"/,&-F'6$F4F,F-F4F1,$F,\"\"$/*&-%$expG6#-%$I ntG6$F1F,F-F9F-,$*&F@F-F,F-F=/-%%DiffG6$**%\"(GF-F@F-F4F-%\")GF-F,FF/* &F@F-F4F-,&-FD6$FFF,F-%#_CGF-/*&-FA6#,$F,F1F-F4F-,&-FD6$,$*&FWF-F,F-F= F,F-FTF-/FV,(Fhn#F=F1FW#F2\"\"%FTF-/F4*&-FA6#,$F,F.F-FjnF-/F6F_o" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "Let's plot a solution curve:" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "dfplot := \+ dfieldplot(diff_eq, y(x), x = 1/2 .. 2, y = 0 ..10, color = khaki):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "soln_plot := implicitplot (1/y = exp(-2*x)*(3/2*exp(2*x)*x-3/4*exp(2*x)), x = 1/2 .. 2, y = 0 .. 10, color = navy, thickness=2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display(\{dfplot, soln_plot\});" }}{PARA 13 "" 1 "" {INLPLOT " 6&-%'CURVESG6]p7$7$$\"1,++++++i!#;$\"1(*********Reb!#:7$$\"1\">w/>w/>' F*$\"1,++++++cF-7$F.7$$\"1-RC!RC!*='F*$\"1M29cxeF*$\"1.++++++wF-Fgo 7$7$$\"1ThX#)H>xeF*F`p7$$\"1qGx:]t^eF*$\"1A9:cm%f6oPYs&F*$\"1.++++++#*F-Fjr7$7$$\"1?%f6oPYs&F*Fcs7$$\"1)[L!>*[% *p&F*$\"1WVk?2qL&*F-7$7$$\"1WWWWWW%p&F*$\"1.++++++'*F-Fis7$F_t7$$\"1e8 i7H!*pcF*$\"1HCDe!)R`**F-7$7$$\"1nmmmmmmcF*$\"#5\"\"!Fet7$7$$FYF*$\"1, +++++7PF-7$$\"1nmmmmmmmF*$\"\"%F`u7$7$$\"1pmmmmmmmF*Fiu7$$\"1B;i@;i@mF *$\"1>*=*=*=*=TF-7$7$$\"1;::::::lF*$\"1*************R%F-F_v7$Fev7$$\"1 j;Q4CBRkF*$\"1\"*)yqs60k%F-7$7$$\"1!*)))))))))))Q'F*$\"1+++++++[F-F[w7 $Faw7$$\"1(pu(*oE)*H'F*$\"1ON[t)[M8&F-7$7$$\"1#G^?G^?G'F*$\"1+++++++_F -Fgw7$F]xF'7$7$$\"1-++++++uF*$\"1**********z!y#F-7$$\"1#Q_4Q_4Q(F*$\"1 +++++++GF-7$Fix7$$\"1]%4Ws/AO(F*$\"1,PR]o>DGF-7$7$$\"1NLLLLL$3(F*$\"1+ ++++++KF-F_y7$Fey7$$\"1mFb5@U%)oF*$\"1C['Hf=Pa$F-7$7$$\"1`=&=&=&=&oF*$ \"1+++++++OF-F[z7$FazFbu7$7$$\"1.++++++!)F*$\"1************RAF-7$$\"1z xxxxxxxF*$\"1+++++++CF-7$F][lFdx7$7$$\"1.++++++')F*$\"1++++++s=F-7$$\" 1OLLLLLL$)F*$\"\"#F`u7$Fi[lFhz7$7$$FdsF*$\"1+++++S!f\"F-7$$\"1pmmmmmm \"*F*$\"1+++++++;F-7$Fd\\lFd[l7$7$$\"1/++++++#*F*Fb\\l7$$\"1hgn7@ND#*F *$\"1&H\\:f)4$e\"F-7$7$$\"1/++++++)*F*$\"1+++++g<9F-F^]l7$Fd]l7$$\"12X 39!p\"G5F-$\"1?mVRK()y7F-7$7$$\"1++++++S5F-$\"1+++++![C\"F-Fj]l7$7$$\" 1,++++++6F-$\"1++++++O6F-7$$\"1cbbbbbb5F-$\"1+++++++7F-7$F[_lF`^l7$Ff^ l7$$\"1&=fz*[C76F-$\"1v(QpMn$=6F-7$7$$\"1,+++++g6F-$\"1+++++g\\5F-Fb_l 7$Fh_l7$$\"1$3/-^v()=\"F-$\"1BhIlK;35F-7$7$$\"1,+++++?7F-$\"1-+++++K'* F*F^`l7$7$Fe`l$\"1.+++++K'*F*7$$\"1\")*[C71`E\"F-$\"1$pMn$=fz*)F*7$7$$ \"1,+++++!G\"F-$\"1)**********zw)F*F]al7$7$$\"1,+++++S8F-$\"1++++++ozF *7$$\"1MLLLLLL8F-$\"1+++++++!)F*7$F^blFcal7$Fial7$$\"16$z8C<0M\"F-$\"1 6$z8CF-$\"1[M5$z8C<&F*7$7$$\"1,+++++S>F-$\"1*********** z3&F*Fgil7$7$F^jl$\"1)**********z3&F*7$$\"1Us^l*oq)>F-$\"1Ts^l*o?'[F*7 $7$$\"1,++++++?F-$FewF*Ffjl-%'COLOURG6&%$RGBG$\")!\\DP\"!\")Fd[m$\")vi obFf[m-%*THICKNESSG6#F]\\l-F$6]dl7%7$$\"+eJE0Y!#5F`u7$$\"+Uot%R&Fb\\mF `u7$$\"+v2\"QA&Fb\\m$\"+qt%*yl!#67%Fc\\m7$$\"+E0@%='Fb\\mF`u7$$\"+fWG8 gFb\\mFi\\m7%F]]m7$$\"+5UotpFb\\mF`u7$$\"+V\"eF!oFb\\mFi\\m7%Fd]m7$$\" +%*y:jxFb\\mF`u7$$\"+F=B#f(Fb\\mFi\\m7%F[^m7$$\"+y:j_&)Fb\\mF`u7$$\"+6 bq\"Q)Fb\\mFi\\m7%Fb^m7$$\"+i_5U$*Fb\\mF`u7$$\"+&>z6<*Fb\\mFi\\m7%Fi^m 7$$\"+&*y:85!\"*F`u7$$\"+$)Glg**Fb\\mFi\\m7%F`_m7$$\"+j_5#4\"Fc_mF`u7$ $\"+cE,v5Fc_mFi\\m7%Fh_m7$$\"+JE0r6Fc_mF`u7$$\"+C+'R:\"Fc_mFi\\m7%F_`m 7$$\"+******\\7Fc_mF`u7$$\"+#R2HB\"Fc_mFi\\m7%Ff`m7$$\"+nt%*G8Fc_mF`u7 $$\"+gZ&=J\"Fc_mFi\\m7%F]am7$$\"+NZ*yS\"Fc_mF`u7$$\"+G@!3R\"Fc_mFi\\m7 %Fdam7$$\"+.@%o[\"Fc_mF`u7$$\"+'\\\\(p9Fc_mFi\\m7%F[bm7$$\"+r%*yl:Fc_m F`u7$$\"+kop[:Fc_mFi\\m7%Fbbm7$$\"+RotW;Fc_mF`u7$$\"+KUkF;Fc_mFi\\m7%F ibm7$$\"+2UoBFc_mF`u7$$\"+/PVV>Fc_mFi\\m7%Fedm7$$\"+zOZR?Fc_mF`u7$$\"+s5QA ?Fc_mFi\\m7%7$$\"+Ow-1YFb\\m$\"+B$eoU&Fb\\m7$$\"+kB(RR&Fb\\m$\"+nuX*4& Fb\\m7$$\"+#4;&H_Fb\\m$\"+QC'p#eFb\\m7%7$$\"+\"ygdR&Fb\\m$\"+G4e_aFb\\ m7$$\"+(e'=$='Fb\\m$\"+i[tt]Fb\\m7$$\"+js!)>gFb\\m$\"+8c%>\"eFb\\m7%7$ $\"+l7`&='Fb\\m$\"+s!\\#yaFb\\m7$$\"+rMOspFb\\m$\"+=n1[]Fb\\m7$$\"+@_2 5oFb\\m$\"+Mu*oz&Fb\\m7%7$$\"+O)Q`(pFb\\m$\"+kb&Q]&Fb\\m7$$\"+pK]hxFb \\m$\"+E-YA]Fb\\m7$$\"+R)>.g(Fb\\m$\"+,C#=y&Fb\\m7%7$$\"+1K=lxFb\\m$\" +'H$RHbFb\\m7$$\"+mig]&)Fb\\m$\"+%\\Ap*\\Fb\\m7$$\"+85a!R)Fb\\m$\"+@]s mdFb\\m7%7$$\"+iS1b&)Fb\\m$\"+g_&[b&Fb\\m7$$\"+yFnR$*Fb\\m$\"+I0Yr\\Fb \\m7$$\"+f'Q2=*Fb\\m$\"+!z4;v&Fb\\m7%7$$\"+f5)\\M*Fb\\m$\"+`XB!e&Fb\\m 7$$\"+:.(G,\"Fc_m$\"+P73Y\\Fb\\m7$$\"+:F\"4(**Fb\\m$\"+*>\"[OdFb\\m7%7 $$\"+$Q$\\85Fc_m$\"+*QCbg&Fb\\m7$$\"+v(p<4\"Fc_m$\"+,9z?\\Fb\\m7$$\"+8 j5w5Fc_m$\"+9PM@dFb\\m7%7$$\"+'>#\\#4\"Fc_m$\"+.\"=2j&Fb\\m7$$\"+)pl1< \"Fc_m$\"+(o(f&*[Fb\\m7$$\"+*)*=^:\"Fc_m$\"+#y,iq&Fb\\m7%7$$\"+.X\\r6F c_m$\"+i\"4el&Fb\\m7$$\"+F\"e&\\7Fc_m$\"+Gm]q[Fb\\m7$$\"+*HHTB\"Fc_m$ \"+=)f5p&Fb\\m7%7$$\"+f-]]7Fc_m$\"+w6z!o&Fb\\m7$$\"+2rWG8Fc_m$\"+9Y_X[ Fb\\m7$$\"+Ws888Fc_m$\"+*>Afn&Fb\\m7%7$$\"+;%4&H8Fc_m$\"+**yl0dFb\\m7$ $\"+'oKtS\"Fc_m$\"+\"*yl?[Fb\\m7$$\"+HG9#R\"Fc_m$\"+kKzgcFb\\m7%7$$\"+ C>_39Fc_m$\"+QKSIdFb\\m7$$\"+9\\@'[\"Fc_m$\"+_D\"fz%Fb\\m7$$\"+eg9r9Fc _m$\"+)Hxck&Fb\\m7%7$$\"+Jx`([\"Fc_m$\"+h7-bdFb\\m7$$\"+VQ4l:Fc_m$\"+H XHrZFb\\m7$$\"+Sp9]:Fc_m$\"+S&y0j&Fb\\m7%7$$\"+$yclc\"Fc_m$\"+.i]zdFb \\m7$$\"+F&pRk\"Fc_m$\"+)e4ou%Fb\\m7$$\"+#[X\"H;Fc_m$\"+l6]:cFb\\m7%7$ $\"+A!zbk\"Fc_m$\"+oC&Q!eFb\\m7$$\"+C?%Gs\"Fc_m$\"+BLYAZFb\\m7$$\"+)pT \"3Fh'=Fc_m$\"+M\"Q/d &Fb\\m7%7$$\"+uUm#)=Fc_m$\"+Cf+weFb\\m7$$\"+!)4Wf>Fc_m$\"+m)4.l%Fb\\m7 $$\"+;l6X>Fc_m$\"+Hn[bbFb\\m7%7$$\"+j')ph>Fc_m$\"+B^u**eFb\\m7$$\"+F8I Q?Fc_m$\"+n1dEYFb\\m7$$\"+mN5C?Fc_m$\"+]ldSbFb\\m7%7$$\"+%o')ph%Fb\\m$ \"+-.H;6Fc_m7$$\"+;L,$Q&Fb\\m$\"+h&G(*))*Fb\\m7$$\"+1d.T_Fb\\m$\"+WMP! 3\"Fc_m7%7$$\"+eCA5aFb\\m$\"+twhD6Fc_m7$$\"+5\\sohFb\\m$\"+^[X'z*Fb\\m 7$$\"+(4u=.'Fb\\m$\"+GzXu5Fc_m7%7$$\"+T`(Q?'Fb\\m$\"+qjlM6Fc_m7$$\"+&R >S&pFb\\m$\"+\")y11(*Fb\\m7$$\"+SxOAoFb\\m$\"+pljo5Fc_m7%7$$\"+Q***y*p Fb\\m$\"+tYQV6Fc_m7$$\"+m@%*QxFb\\m$\"+^[y='*Fb\\m7$$\"+GU`7wFb\\m$\"+ Y#HH1\"Fc_m7%7$$\"+B*\\Az(Fb\\m$\"+!)ey^6Fc_m7$$\"+]&RN_)Fb\\m$\"+wFxM &*Fb\\m7$$\"+kNR-%)Fb\\m$\"+_JNd5Fc_m7%7$$\"+\"4zoe)Fb\\m$\"+<\"[)f6Fc _m7$$\"+\\x&yI*Fb\\m$\"+9/:a%*Fb\\m7$$\"+#\\n>>*Fb\\m$\"+>F#>0\"Fc_m7% 7$$\"+!HU%>45Fc_m$\"+=9*pP*Fb\\m7$$\"+a)y 7)**Fb\\m$\"+\\'\\m/\"Fc_m7%7$$\"+<'zw,\"Fc_m$\"+B.$\\<\"Fc_m7$$\"+TNe (3\"Fc_m$\"+_$GLI*Fb\\m7$$\"++^.x5Fc_m$\"+9IaT5Fc_m7%7$$\"+y**>(4\"Fc_ m$\"+Fu%>=\"Fc_m7$$\"+;z&f;\"Fc_m$\"+9t:L#*Fb\\m7$$\"+I2#f:\"Fc_m$\"+= %4m.\"Fc_m7%7$$\"+,:tw6Fc_m$\"+x)=')=\"Fc_m7$$\"+H6KW7Fc_m$\"+6GWm\"*F b\\m7$$\"+pqyM7Fc_m$\"+*>`=.\"Fc_m7%7$$\"+&oqiD\"Fc_m$\"+))3&\\>\"Fc_m 7$$\"+\"owEK\"Fc_m$\"+/F7.\"*Fb\\m7$$\"+Njj88Fc_m$\"+pmFF5Fc_m7%7$$\"+ fV\"eL\"Fc_m$\"+e=&4?\"Fc_m7$$\"+Vx-,9Fc_m$\"+(*H6V!*Fb\\m7$$\"+U1Z#R \"Fc_m$\"+_.)G-\"Fc_m7%7$$\"+!of`T\"Fc_m$\"+D>j17Fc_m7$$\"+erPz9Fc_m$ \"+JBJ')*)Fb\\m7$$\"+\")>Hr9Fc_m$\"+PKm=5Fc_m7%7$$\"+NT!\\\\\"Fc_m$\"+ [D+77Fc_m7$$\"+Rusd:Fc_m$\"+(41E$*)Fb\\m7$$\"+1A5]:Fc_m$\"+)Rl\"Fc_m$\"+!yl=A\"Fc_m7$$\"+,\"RWr\"Fc_ m$\"+\"ytR$))Fb\\m7$$\"+Dgp2Fc_ m$\"+Fc(fq)Fb\\m7$$\"+`:/W>Fc_m$\"+#G4$p**Fb\\m7%7$$\"+*>\\?(>Fc_m$\"+ XSXQ7Fc_m7$$\"+\"z]z-#Fc_m$\"+I64o')Fb\\m7$$\"+%3;G-#Fc_m$\"+6EdQ**Fb \\m7%7$$\"+[!Gdl%Fb\\m$\"+GFW`Fb\\m$\"+5I?]9Fc_m7$$\"+ epZV_Fb\\m$\"+6'HLc\"Fc_m7%7$$\"+R_VeaFb\\m$\"+u&*GA :Fc_m7%7$$\"+V9Iq%*Fb\\m$\"+6I0t\"y8Fc_m7$$\"+[eiu5Fc_m$\"+*>&f2:Fc_m7%7$$\"+wH:26Fc_m$ \"+!\\scy\"Fc_m7$$\"+=\\+c6Fc_m$\"+[AAs8Fc_m7$$\"+a.=`6Fc_m$\"+-oW-:Fc _m7%7$$\"+C47(=\"Fc_m$\"+Y]&3z\"Fc_m7$$\"+1<$RB\"Fc_m$\"+#pRqO\"Fc_m7$ $\"+7MuJ7Fc_m$\"+#R2y\\\"Fc_m7%7$$\"+Jz-n7Fc_m$\"+,,U&z\"Fc_m7$$\"+N%> >J\"Fc_m$\"+PYZi8Fc_m7$$\"+nyJ58Fc_m$\"+m'>O\\\"Fc_m7%7$$\"+Xj(oM\"Fc_ m$\"+y:X*z\"Fc_m7$$\"+dd'**Q\"Fc_m$\"+gJWe8Fc_m7$$\"+Lb!*)Q\"Fc_m$\"+F @$)*[\"Fc_m7%7$$\"+$3pmU\"Fc_m$\"+%o@I!=Fc_m7$$\"+bx1o9Fc_m$\"+aI([N\" Fc_m7$$\"+mu]n9Fc_m$\"+t*)R'[\"Fc_m7%7$$\"+i$4k]\"Fc_m$\"+;B>1=Fc_m7$$ \"+7AAY:Fc_m$\"+ACq^8Fc_m7$$\"+jT7Y:Fc_m$\"+Y(zK[\"Fc_m7%7$$\"+705'e\" Fc_m$\"+Ek,4=Fc_m7$$\"+)zDWi\"Fc_m$\"+7$y)[8Fc_m7$$\"+?dvC;Fc_m$\"+v)Q /[\"Fc_m7%7$$\"+Zeul;Fc_m$\"+(GR:\"=Fc_m7$$\"+*>vEq\"Fc_m$\"+^aNY8Fc_m 7$$\"+d>S.n4y\"Fc_m$\"+F^4W8Fc_m7$$\"+*\\i?y\"Fc_m$\"+/8Zv9Fc_m7%7$$\"+-=\"\\#= Fc_m$\"+P0$e\"=Fc_m7$$\"+;()Hf=Fc_m$\"+,U1U8Fc_m7$$\"+]otg=Fc_m$\"+$Q$ Ht9Fc_m7%7$$\"+)QQW!>Fc_m$\"+x/m<=Fc_m7$$\"+momP>Fc_m$\"+iUBS8Fc_m7$$ \"+JWUR>Fc_m$\"+n/Hr9Fc_m7%7$$\"+_5$R)>Fc_m$\"+JQJ>=Fc_m7$$\"+Q*og,#Fc _m$\"+24eQ8Fc_m7$$\"+CY7=?Fc_m$\"+5UWp9Fc_m7%7$$\"+T?\\?ZFb\\m$\"+Dc3 \"H#Fc_m7$$\"+fz]z_Fb\\m$\"+$pS%>>Fc_m7$$\"+()3;G_Fb\\m$\"+T))[Y?Fc_m7 %7$$\"+lg0JbFb\\m$\"+]3>/BFc_m7$$\"+.8*y/'Fb\\m$\"+oaL1>Fc_m7$$\"+w5f5 gFb\\m$\"+)GVb.#Fc_m7%7$$\"+&zy'RjFb\\m$\"+ukc9BFc_m7$$\"+Tf@=oFb\\m$ \"+W)ff*=Fc_m7$$\"+`$)4$z'Fb\\m$\"+L*ok-#Fc_m7%7$$\"+UZNYrFb\\m$\"+>#H GK#Fc_m7$$\"+it[!f(Fb\\m$\"+*4(p()=Fc_m7$$\"+-r\"fd(Fb\\m$\"+=q\"*=?Fc _m7%7$$\"+%>/7&zFb\\m$\"+x;YHBFc_m7$$\"+y_ek$)Fb\\m$\"+TY1\")=Fc_m7$$ \"+#4g\"f$)Fb\\m$\"+rQf7?Fc_m7%7$$\"+e,Sa()Fb\\m$\"+;K$[L#Fc_m7$$\"+#o O.9*Fb\\m$\"+-Jpv=Fc_m7$$\"+Xx'G9*Fb\\m$\"+I7E2?Fc_m7%7$$\"+Z%Ghb*Fb\\ m$\"+\")RARBFc_m7$$\"+hdb<**Fb\\m$\"+PBIr=Fc_m7$$\"+g(Rq#**Fb\\m$\"+)G HF+#Fc_m7%7$$\"+qnlN5Fc_m$\"+Ph%GM#Fc_m7$$\"+)Q1'p5Fc_m$\"+\"=!on=Fc_m 7$$\"+Ua;r5Fc_m$\"+wz%))*>Fc_m7%7$$\"+f!)e:6Fc_m$\"+j3'eM#Fc_m7$$\"+N) pv9\"Fc_m$\"+bamk=Fc_m7$$\"+\"*zm\\6Fc_m$\"+(z)\\&*>Fc_m7%7$$\"+)4@a> \"Fc_m$\"+28R[BFc_m7$$\"+K:jD7Fc_m$\"+6]8i=Fc_m7$$\"+(33#G7Fc_m$\"+\\z e#*>Fc_m7%7$$\"+0%o^F\"Fc_m$\"+VA`]BFc_m7$$\"+h*yPI\"Fc_m$\"+vS**f=Fc_ m7$$\"+&=#y18Fc_m$\"+L3/!*>Fc_m7%7$$\"+y2%[N\"Fc_m$\"+)>dBN#Fc_m7$$\"+ C8+#Q\"Fc_m$\"+?\"p\"e=Fc_m7$$\"+?pQ&Q\"Fc_m$\"+lxz()>Fc_m7%7$$\"+!\\Z WV\"Fc_m$\"+\"pBRN#Fc_m7$$\"+[$*Gg9Fc_m$\"+GEgc=Fc_m7$$\"+#>>SY\"Fc_m$ \"+y1\"e)>Fc_m7%7$$\"+%\\'*R^\"Fc_m$\"+%4x_N#Fc_m7$$\"+!3N'Q:Fc_m$\"+D #\\_&=Fc_m7$$\"+#>wEa\"Fc_m$\"+*eSS)>Fc_m7%7$$\"+8Y\\$f\"Fc_m$\"+'\\`k N#Fc_m7$$\"+(pJqh\"Fc_m$\"+AG2a=Fc_m7$$\"+2aN@;Fc_m$\"+lcX#)>Fc_m7%7$$ \"+6x%Hn\"Fc_m$\"+J=[dBFc_m7$$\"+NLZ&p\"Fc_m$\"+([WI&=Fc_m7$$\"+&fa+q \"Fc_m$\"+H(H5)>Fc_m7%7$$\"+R3O_Fc_m7%7$$\"+e$Q<$=Fc_m$\"+aM=fBFc_ m7$$\"+g@Z_=Fc_m$\"+kGM^=Fc_m7$$\"+r^]d=Fc_m$\"+XFc_m7%7$$\"+\\S36 >Fc_m$\"+f8*)fBFc_m7$$\"+07-J>Fc_m$\"+f\\j]=Fc_m7$$\"+UKDO>Fc_m$\"++l] x>Fc_m7%7$$\"+(>,/*>Fc_m$\"+a?_gBFc_m7$$\"+$z)f4?Fc_m$\"+lU+]=Fc_m7$$ \"++Y,:?Fc_m$\"+0E`w>Fc_m7%7$$\"+Qoz'y%Fb\\m$\"+y.0`GFc_m7$$\"+iJ?8_Fb \\m$\"+?v55CFc_m7$$\"+r_$R?&Fb\\m$\"+A8aTDFc_m7%7$$\"+FP6)f&Fb\\m$\"+h luhGFc_m7$$\"+TO$3)fFb\\m$\"+P8T,CFc_m7$$\"+._G%)fFb\\m$\"+j,(H`#Fc_m7 %7$$\"+<3!fS'Fb\\m$\"+s>5oGFc_m7$$\"+>R*>v'Fb\\m$\"+Ef0&R#Fc_m7$$\"+)p edw'Fb\\m$\"+\"\\9j_#Fc_m7%7$$\"+dK\"3@(Fb\\m$\"+T0&G(GFc_m7$$\"+Z)Gg_ (Fb\\m$\"+dtI!R#Fc_m7$$\"+<&f#[vFb\\m$\"+()*[5_#Fc_m7%7$$\"+)=-M,)Fb\\ m$\"+[EZwGFc_m7$$\"+&G(Q-$)Fb\\m$\"+^_o'Q#Fc_m7$$\"+8`lJ$)Fb\\m$\"+D%4 o^#Fc_m7%7$$\"+U169))Fb\\m$\"+V!)GzGFc_m7$$\"+)>E13*Fb\\m$\"+b)pQQ#Fc_ m7$$\"+)z9e6*Fb\\m$\"+p1M8DFc_m7%7$$\"+<()G8'*Fb\\m$\"+;Q^\")GFc_m7$$ \"+#\\&Rg)*Fb\\m$\"+#3W;Q#Fc_m7$$\"+\")3i+**Fb\\m$\"+&Gh/^#Fc_m7%7$$\" +(>@6/\"Fc_m$\"+'Q+L)GFc_m7$$\"+h>9k5Fc_m$\"+7v&)zBFc_m7$$\"+ttfo5Fc_m $\"+i+/3DFc_m7%7$$\"+\"y437\"Fc_m$\"+eSv%)GFc_m7$$\"+8\"[B9\"Fc_m$\"+S QSyBFc_m7$$\"+%**yr9\"Fc_m$\"+)[!)f]#Fc_m7%7$$\"+y=T+7Fc_m$\"+r8&f)GFc _m7$$\"+_2k?7Fc_m$\"+Fl?xBFc_m7$$\"+Q+!eA\"Fc_m$\"+7/@/DFc_m7%7$$\"+!G T*z7Fc_m$\"+,%[p)GFc_m7$$\"+'31!*H\"Fc_m$\"+(\\4iP#Fc_m7$$\"+*yaWI\"Fc _m$\"+_]n-DFc_m7%7$$\"+,\"4%f8Fc_m$\"+%*oy()GFc_m7$$\"+,IVx8Fc_m$\"+/5 PvBFc_m7$$\"+5&QJQ\"Fc_m$\"+;AL,DFc_m7%7$$\"+oV#)Q9Fc_m$\"+(Q)\\))GFc_ m7$$\"+qC\"fX\"Fc_m$\"+6&fYP#Fc_m7$$\"+ns%=Y\"Fc_m$\"+v*[,]#Fc_m7%7$$ \"+wW>=:Fc_m$\"+Kq5*)GFc_m7$$\"+)4PW`\"Fc_m$\"+m30uBFc_m7$$\"+qxdS:Fc_ m$\"+:$*4*\\#Fc_m7%7$$\"+Db_(f\"Fc_m$\"+c:j*)GFc_m7$$\"+&y+Ih\"Fc_m$\" +Uj_tBFc_m7$$\"+msK>;Fc_m$\"+[C;)\\#Fc_m7%7$$\"+)eAon\"Fc_m$\"+Zm3!*GF c_m7$$\"+e%)f\"p\"Fc_m$\"+_72tBFc_m7$$\"+FM4)p\"Fc_m$\"+$f@t\\#Fc_m7%7 $$\"+8**3cFc_m$\"+\\1 9\"*GFc_m7$$\"+HhbF>Fc_m$\"+\\s,sBFc_m7$$\"+%ftW$>Fc_m$\"+K*\\_\\#Fc_m 7%7$$\"+Qmu$*>Fc_m$\"+2PT\"*GFc_m7$$\"+_LD1?Fc_m$\"+#>W)[.MFc_m7$$\"+i(o7$fFb\\m$\"+\"G,B\"HFc_m7$$\"+Rs'>'fFb\\m$\"+\") )yA/$Fc_m7%7$$\"+w3J_kFb\\m$\"+HG92MFc_m7$$\"+gQe0nFb\\m$\"+\\mk3HFc_m 7$$\"+%o;Uu'Fb\\m$\"+?.oPIFc_m7%7$$\"+@R:asFb\\m$\"+Uby4MFc_m7$$\"+$=) o#[(Fb\\m$\"+OR+1HFc_m7$$\"+:\"ow_(Fb\\m$\"+v.7MIFc_m7%7$$\"+9*zQ0)Fb \\m$\"+s@v6MFc_m7$$\"+f&4>E)Fb\\m$\"+1t./HFc_m7$$\"+dj17$)Fb\\m$\"+.mH JIFc_m7%7$$\"+d5(>&))Fb\\m$\"+@?D8MFc_m7$$\"+$ylF/*Fb\\m$\"+eu`-HFc_m7 $$\"+%\\;s4*Fb\\m$\"+l*4!HIFc_m7%7$$\"+?'y(['*Fb\\m$\"+R-U9MFc_m7$$\"+ )e0\\#)*Fb\\m$\"+R#p8!HFc_m7$$\"+W+(H))*Fb\\m$\"+'GDr-$Fc_m7%7$$\"+\"G cW/\"Fc_m$\"+#*oM:MFc_m7$$\"+xo!31\"Fc_m$\"+'eU/!HFc_m7$$\"+D8#p1\"Fc_ m$\"+N\"[b-$Fc_m7%7$$\"+f>&R7\"Fc_m$\"+(p$4;MFc_m7$$\"+Nf?R6Fc_m$\"+\" y&p**GFc_m7$$\"+8eeX6Fc_m$\"+d3@CIFc_m7%7$$\"+())zL?\"Fc_m$\"+0Sq;MFc_ m7$$\"+VFn<7Fc_m$\"+ta3**GFc_m7$$\"+'f$GC7Fc_m$\"+')Q1BIFc_m7%7$$\"+-< v#G\"Fc_m$\"+R*3sT$Fc_m7$$\"+kc>'H\"Fc_m$\"+R0e)*GFc_m7$$\"+V#4II\"Fc_ m$\"+$=q?-$Fc_m7%7$$\"+gl2i8Fc_m$\"+)GJwT$Fc_m7$$\"+Ubwu8Fc_m$\"+!>e\" )*GFc_m7$$\"+=%eIFc_m7%7$$\"+Ub$)*f\"Fc_m$\"+;Jb=MFc_m7$$\"+o2p5;Fc_m$\"+ijB(*GFc_m 7$$\"+K_6=;Fc_m$\"+s2:>IFc_m7%7$$\"+YG.z;Fc_m$\"+(**y(=MFc_m7$$\"++#)Q *o\"Fc_m$\"+\"[5q*GFc_m7$$\"+g$Hpp\"Fc_m$\"+Shg=IFc_m7%7$$\"+@$3#eMFc_m7$$\"+Je%o%=Fc_m$\"+e9k'*GFc_m7$$\" +,,fa=Fc_m$\"++%ow,$Fc_m7%7$$\"+KU];>Fc_m$\"+=)*H>MFc_m7$$\"+A5gD>Fc_m $\"+g'*['*GFc_m7$$\"++UVL>Fc_m$\"+R?EFc_m$\"+=UV> MFc_m7$$\"+&4rV+#Fc_m$\"+g_N'*GFc_m7$$\"+%3'G7?Fc_m$\"+V.*o,$Fc_m7%7$$ \"+Xb;x[Fb\\m$\"+UGIMRFc_m7$$\"+cW$G7&Fb\\m$\"+;#=TV$Fc_m7$$\"+%>IM;&F b\\m$\"+tP)Gc$Fc_m7%7$$\"+*\\f?o&Fb\\m$\"+A!Qu$RFc_m7$$\"+py)o*eFb\\m$ \"+OI)4V$Fc_m7$$\"+skLXfFb\\m$\"+@h`eNFc_m7%7$$\"+PLi$['Fb\\m$\"+\")*z &RRFc_m7$$\"+*RrUn'Fb\\m$\"+x5%)GMFc_m7$$\"+F%e(GnFb\\m$\"+KmIbNFc_m7% 7$$\"+.D!GG(Fb\\m$\"+BO5TRFc_m7$$\"+,'RSX(Fb\\m$\"+NuJFMFc_m7$$\"+#f+L ^(Fb\\m$\"+m^#Gb$Fc_m7%7$$\"+9YA!3)Fb\\m$\"+-RAURFc_m7$$\"+e[cN#)Fb\\m $\"+cr>EMFc_m7$$\"+Cxo)H)Fb\\m$\"+W_'3b$Fc_m7%7$$\"+e\">j())Fb\\m$\"+u 02VRFc_m7$$\"+#o<%=!*Fb\\m$\"+%[]`U$Fc_m7$$\"+m\\s%3*Fb\\m$\"+:?FU$Fc_m7$$\"+'*)* of9Fc_m$\"+TMMVNFc_m7%7$$\"+He5A:Fc_m$\"+su'e%RFc_m7$$\"+Xd_I:Fc_m$\"+ 'e`DU$Fc_m7$$\"+:\\^Q:Fc_m$\"+i4(Ga$Fc_m7%7$$\"+e!e7g\"Fc_m$\"+j.,YRFc _m7$$\"+_#o#4;Fc_m$\"+&p5CU$Fc_m7$$\"+)[^th\"Fc_m$\"+5&[Ca$Fc_m7%7$$\" +l8R!o\"Fc_m$\"+CQ8YRFc_m7$$\"+\"oH!)o\"Fc_m$\"+MsGAMFc_m7$$\"+h!)>'p \"Fc_m$\"+6'o?a$Fc_m7%7$$\"+W#3&fFc_m$\"+NzTYRFc_m7$$\"+iXSC>Fc_m$\"+BJ+AMFc_m7$$\"+4fyK>Fc_m$\"+= )G6a$Fc_m7%7$$\"+v%zn*>Fc_m$\"+D6\\YRFc_m7$$\"+:0A.?Fc_m$\"+L*H>U$Fc_m 7$$\"+6:m6?Fc_m$\"+'Ho3a$Fc_m7%7$$\"+??,/\\Fb\\m$\"+9_ylWFc_m7$$\"+!)z )f4&Fb\\m$\"+CuEbRFc_m7$$\"+^g9]^Fb\\m$\"+kdz\"3%Fc_m7%7$$\"+(*\\%fq&F b\\m$\"+<]snWFc_m7$$\"+rB+teFb\\m$\"+@wK`RFc_m7$$\"++HGLfFb\\m$\"+s$>' ySFc_m7%7$$\"+A!o]]'Fb\\m$\"+f97Fc_m$\"+')zw[RFc_m7$$\"+OukA7Fc_m$\"+)y)))oSFc_m7%7$$\"+DXl&G \"Fc_m$\"+9'\\CZ%Fc_m7$$\"+TGH$H\"Fc_m$\"+CIg[RFc_m7$$\"+@7Y,8Fc_m$\"+ ,WQoSFc_m7%7$$\"+S.#[O\"Fc_m$\"+&4(esWFc_m7$$\"+i<-s8Fc_m$\"+WbY[RFc_m 7$$\"+)))*G!Q\"Fc_m$\"+tB%z1%Fc_m7%7$$\"+2E'RW\"Fc_m$\"+mGqsWFc_m7$$\" +JUx]9Fc_m$\"+s(\\$[RFc_m7$$\"+\"4J\"f9Fc_m$\"+,>bnSFc_m7%7$$\"+D\\3B: Fc_m$\"+i7!GZ%Fc_m7$$\"+\\maH:Fc_m$\"+w8D[RFc_m7$$\"+bH)z`\"Fc_m$\"+FX ?nSFc_m7%7$$\"++->-;Fc_m$\"+*e&)GZ%Fc_m7$$\"+5hL3;Fc_m$\"+\\q;[RFc_m7$ $\"+aR%oh\"Fc_m$\"+ON*o1%Fc_m7%7$$\"++3G\"o\"Fc_m$\"+.%eHZ%Fc_m7$$\"+Y -9(o\"Fc_m$\"+NU4[RFc_m7$$\"+UGr&p\"Fc_m$\"+KNhmSFc_m7%7$$\"+v'e.w\"Fc _m$\"+1<-tWFc_m7$$\"+2r&fw\"Fc_m$\"+K4.[RFc_m7$$\"+)e)euFc_m$\"+/e7tWFc_m7$$\"+*yAO#>Fc_m$ \"+Mo#z%RFc_m7$$\"+dtNK>Fc_m$\"+]$>f1%Fc_m7%7$$\"+\")3`(*>Fc_m$\"+#*)o JZ%Fc_m7$$\"+4\"pC+#Fc_m$\"+YP)y%RFc_m7$$\"+[!\\7,#Fc_m$\"+1lslSFc_m7% 7$$\"+))3IB\\Fb\\m$\"+^X)\\*\\Fc_m7$$\"+7\"*pw]Fb\\m$\"+n'*pyWFc_m7$$ \"+Q3HS^Fb\\m$\"+4=E.YFc_m7%7$$\"+kM\"Hs&Fb\\m$\"+;>B'*\\Fc_m7$$\"+/R. ceFb\\m$\"+-BXxWFc_m7$$\"+hO[CfFb\\m$\"+`Z'3g%Fc_m7%7$$\"+7c=?lFb\\m$ \"+\\y1(*\\Fc_m7$$\"+C\"4xj'Fb\\m$\"+pjhwWFc_m7$$\"+!>\\)4nFb\\m$\"+Y5 4*f%Fc_m7%7$$\"+-p$eJ(Fb\\m$\"+&eaw*\\Fc_m7$$\"+-_+@uFb\\m$\"+L'HgZ%Fc _m7$$\"+w-/'\\(Fb\\m$\"+t(Gxf%Fc_m7%7$$\"+m:K5\")Fb\\m$\"+h=3)*\\Fc_m7 $$\"+1zY0#)Fb\\m$\"+dBgvWFc_m7$$\"+EI$GG)Fb\\m$\"+]8l'f%Fc_m7%7$$\"+Z' RR!*)Fb\\m$\"+$[-%)*\\Fc_m7$$\"+$>(z!**)Fb\\m$\"+NhL9\"Fc_m$\"+_$RRf%Fc_m7%7$$\"+7vI27Fc_m$\"+UO7**\\Fc_m7$$\"+=^u8 7Fc_m$\"+w0cuWFc_m7$$\"+$*o=A7Fc_m$\"+$['\\$f%Fc_m7%7$$\"+c2X'G\"Fc_m$ \"+4sA**\\Fc_m7$$\"+5m\\#H\"Fc_m$\"+5qXuWFc_m7$$\"+'3F5I\"Fc_m$\"+-86$ f%Fc_m7%7$$\"+(erbO\"Fc_m$\"+nMJ**\\Fc_m7$$\"+:0Fr8Fc_m$\"+_2PuWFc_m7$ $\"+P$z)z8Fc_m$\"+!HtFf%Fc_m7%7$$\"+OOnW9Fc_m$\"+kgQ**\\Fc_m7$$\"+-K1] 9Fc_m$\"+a\")HuWFc_m7$$\"+Df%Fc_m7%7$$\"+\"G$*=o\"Fc_m$\"+zha**\\Fc_m7$$\"+lx_ 'o\"Fc_m$\"+R!QTZ%Fc_m7$$\"+sdP&p\"Fc_m$\"+3Vv\"f%Fc_m7%7$$\"+sS%4w\"F c_m$\"+;ee**\\Fc_m7$$\"+55;`=Fc_m$\"+V@Q\"f%Fc_m7%7$$\"+i-->>Fc_m$\"+u4l**\\Fc_m7$$\"+#* \\3B>Fc_m$\"+WK.uWFc_m7$$\"+&Gg?$>Fc_m$\"+'4?7f%Fc_m7%7$$\"+bw/)*>Fc_m $\"+Ozn**\\Fc_m7$$\"+NB&>+#Fc_m$\"+$G1SZ%Fc_m7$$\"+!Hj4,#Fc_m$\"+N92\" f%Fc_m7%7$$\"+NkYP\\Fb\\m$\"+dE*H_&Fc_m7$$\"+lN`i]Fb\\m$\"+TJK.]Fc_m7$ $\"+rP*G8&Fb\\m$\"+_rDE^Fc_m7%7$$\"+vVHNdFb\\m$\"+G_#Q_&Fc_m7$$\"+$*Hl VeFb\\m$\"+q0\\-]Fc_m7$$\"+7H%z\"fFb\\m$\"+>FRC^Fc_m7%7$$\"+Oz;JlFb\\m $\"+?4QCbFc_m7$$\"++osEmFb\\m$\"+y[$>+&Fc_m7$$\"+Kj*Rq'Fb\\m$\"+.5,B^F c_m7%7$$\"+DtpDtFb\\m$\"+u)pZ_&Fc_m7$$\"+zZ96uFb\\m$\"+Cfa,]Fc_m7$$\"+ `$\\2\\(Fb\\m$\"+ay%>7&Fc_m7%7$$\"+mQE>\")Fb\\m$\"+gD0DbFc_m7$$\"+2c_' >)Fb\\m$\"+QKE,]Fc_m7$$\"+Z%3!y#)Fb\\m$\"+Ja5@^Fc_m7%7$$\"+pw67*)Fb\\m $\"+uVEDbFc_m7$$\"+r\">E)*)Fb\\m$\"+C90,]Fc_m7$$\"+w]kl!*Fb\\m$\"+#)>U ?^Fc_m7%7$$\"+2%HWq*Fb\\m$\"+NrUDbFc_m7$$\"+,[Dp(*Fb\\m$\"+k'))3+&Fc_m 7$$\"+b1d`)*Fb\\m$\"+\"pc)>^Fc_m7%7$$\"+W>j\\5Fc_m$\"+z[bDbFc_m7$$\"+9 7jb5Fc_m$\"+>4w+]Fc_m7$$\"+@A^Fc_m7%7$$\"+.vyG6Fc_m$\"+ lplDbFc_m7$$\"+\"RqV8\"Fc_m$\"+L)e1+&Fc_m7$$\"+v`+V6Fc_m$\"+pm(*=^Fc_m 7%7$$\"+)4;z?\"Fc_m$\"+C)Rd_&Fc_m7$$\"+Kl887Fc_m$\"+ufd+]Fc_m7$$\"+(4` =A\"Fc_m$\"+Wwi=^Fc_m7%7$$\"+RE-(G\"Fc_m$\"+%*z!e_&Fc_m7$$\"+FZ#>H\"Fc _m$\"+/y]+]Fc_m7$$\"+tFr+8Fc_m$\"+/PK=^Fc_m7%7$$\"+:46m8Fc_m$\"+]Z'e_& Fc_m7$$\"+(=J2P\"Fc_m$\"+[5X+]Fc_m7$$\"+wBez8Fc_m$\"+zm0=^Fc_m7%7$$\"+ $*Q=X9Fc_m$\"+.D\"f_&Fc_m7$$\"+XHb\\9Fc_m$\"+&H./+&Fc_m7$$\"+:.Ye9Fc_m $\"+_-#y6&Fc_m7%7$$\"+MRCC:Fc_m$\"+gI&f_&Fc_m7$$\"+SwQG:Fc_m$\"+QFO+]F c_m7$$\"+?`MP:Fc_m$\"+p%4w6&Fc_m7%7$$\"+OHH.;Fc_m$\"+'z()f_&Fc_m7$$\"+ uLB2;Fc_m$\"+-!G.+&Fc_m7$$\"+ljB;;Fc_m$\"+%Q?u6&Fc_m7%7$$\"+WCL#o\"Fc_ m$\"+ux,EbFc_m7$$\"+-')3'o\"Fc_m$\"+C!)H+]Fc_m7$$\"+:E8&p\"Fc_m$\"+@) \\s6&Fc_m7%7$$\"+FPOhF+]Fc_m 7$$\"+#QLSx\"Fc_m$\"+#>&4<^Fc_m7%7$$\"+RyQS=Fc_m$\"+/m1EbFc_m7$$\"+zE# Q%=Fc_m$\"+%>\\-+&Fc_m7$$\"+\"4QH&=Fc_m$\"+pV&p6&Fc_m7%7$$\"+hcS>>Fc_m $\"+Rm3EbFc_m7$$\"+$f*pA>Fc_m$\"+f\"H-+&Fc_m7$$\"+ji%=$>Fc_m$\"+(eDo6& Fc_m7%7$$\"+MzT)*>Fc_m$\"+^V5EbFc_m7$$\"+c?e,?Fc_m$\"+Z9@+]Fc_m7$$\"+& \\d2,#Fc_m$\"+ptq;^Fc_m7%7$$\"+oD6[\\Fb\\m$\"+v\"[.0'Fc_m7$$\"+Ku)=0&F b\\m$\"+.#*fGbFc_m7$$\"+ZuCF^Fb\\m$\"+u!4-l&Fc_m7%7$$\"++JcWdFb\\m$\"+ DG#40'Fc_m7$$\"+oUQMeFb\\m$\"+`X-GbFc_m7$$\"+T3)H\"fFb\\m$\"+Z/s[cFc_m 7%7$$\"+@#o$RlFb\\m$\"+8aI^gFc_m7$$\"+:l_=mFb\\m$\"+m>kFbFc_m7$$\"+Q^d *p'Fb\\m$\"+`\\hZcFc_m7%7$$\"+Zk/LtFb\\m$\"+ZFd^gFc_m7$$\"+dcz.uFb\\m$ \"+JYPFbFc_m7$$\"+]^w'[(Fb\\m$\"+?EwYcFc_m7%7$$\"+B)>f7)Fb\\m$\"+2ow^g Fc_m7$$\"+\\'p)*=)Fb\\m$\"+r0=FbFc_m7$$\"+DSQu#)Fb\\m$\"+vf3YcFc_m7%7$ $\"+v')>=*)Fb\\m$\"+%37>0'Fc_m7$$\"+l\"Ql(*)Fb\\m$\"+%HNq_&Fc_m7$$\"+$ p@B1*Fb\\m$\"+xg`XcFc_m7%7$$\"+zg-5(*Fb\\m$\"+UO-_gFc_m7$$\"+H\"eOw*Fb \\m$\"+OP#p_&Fc_m7$$\"+#o-0&)*Fb\\m$\"+Q03XcFc_m7%7$$\"+q-:]5Fc_m$\"+a 66_gFc_m7$$\"+))G6b5Fc_m$\"+Ci$o_&Fc_m7$$\"+bt)Q1\"Fc_m$\"+(4(pWcFc_m7 %7$$\"+Q,FH6Fc_m$\"+f5=_gFc_m7$$\"+cx)Q8\"Fc_m$\"+>jwEbFc_m7$$\"+R&RF9 \"Fc_m$\"+i*pVk&Fc_m7%7$$\"+:wO37Fc_m$\"+zxB_gFc_m7$$\"+:]o77Fc_m$\"+* f4n_&Fc_m7$$\"+CRg@7Fc_m$\"+Aw3WcFc_m7%7$$\"+)yYuG\"Fc_m$\"+JWG_gFc_m7 $$\"+y0]\"H\"Fc_m$\"+ZHmEbFc_m7$$\"+5$y/I\"Fc_m$\"+&\\TQk&Fc_m7%7$$\"+ 53^m8Fc_m$\"+kKK_gFc_m7$$\"+#HJ.P\"Fc_m$\"+9TiEbFc_m7$$\"+$*4Oz8Fc_m$ \"+`]iVcFc_m7%7$$\"+\\@cX9Fc_m$\"+IfN_gFc_m7$$\"+*ou\"\\9Fc_m$\"+[9fEb Fc_m7$$\"+N1De9Fc_m$\"+[KVVcFc_m7%7$$\"+kFgC:Fc_m$\"+pOQ_gFc_m7$$\"+5) G!G:Fc_m$\"+4PcEbFc_m7$$\"+th9P:Fc_m$\"+4@EVcFc_m7%7$$\"+KUj.;Fc_m$\"+ CuS_gFc_m7$$\"+y?*og\"Fc_m$\"+a*Rl_&Fc_m7$$\"+\\n/;;Fc_m$\"+t%3Jk&Fc_m 7%7$$\"+Myl#o\"Fc_m$\"+BzU_gFc_m7$$\"+7Kw&o\"Fc_m$\"+b%>l_&Fc_m7$$\"+i ;&\\p\"Fc_m$\"+$zpHk&Fc_m7%7$$\"+DYnh>Fc_m$\"+.]Z_gFc_m7$$\"+KTTA>Fc_m$\"+vBZEbFc_m7$$\"+KroJ>Fc_m$\"+ gWiUcFc_m7%7$$\"+t@p)*>Fc_m$\"+6r[_gFc_m7$$\"+ylFc_m7$$\"+# p!=)R(Fb\\m$\"+@0Q`gFc_m7$$\"+\\xp$[(Fb\\m$\"+to'><'Fc_m7%7$$\"+!)4+J \")Fb\\m$\"+**eLylFc_m7$$\"+#\\)y%=)Fb\\m$\"+fIC`gFc_m7$$\"+h!)fr#)Fb \\m$\"+'G69<'Fc_m7%7$$\"+P!QG#*)Fb\\m$\"+Y(Q%ylFc_m7$$\"+.))*=(*)Fb\\m $\"+7-9`gFc_m7$$\"+6.xf!*Fb\\m$\"+y!f4<'Fc_m7%7$$\"+'*QH9(*Fb\\m$\"+*o <&ylFc_m7$$\"+7.Rf(*Fb\\m$\"+p71`gFc_m7$$\"+I(\\\"[)*Fb\\m$\"+cReqhFc_ m7%7$$\"+y`a]5Fc_m$\"+&fz&ylFc_m7$$\"+!yN8\"Fc _m$\"+D*\\H0'Fc_m7$$\"+if`U6Fc_m$\"+>y**phFc_m7%7$$\"+4;r37Fc_m$\"+Q\" p'ylFc_m7$$\"+@5M77Fc_m$\"+?)4H0'Fc_m7$$\"+=KT@7Fc_m$\"+hXwphFc_m7%7$$ \"+o)pxG\"Fc_m$\"+>@qylFc_m7$$\"+)\\x6H\"Fc_m$\"+So(G0'Fc_m7$$\"+[*)H+ 8Fc_m$\"+W5cphFc_m7%7$$\"+l`\"oO\"Fc_m$\"+n&H(ylFc_m7$$\"+Pn-q8Fc_m$\" +\"R\\G0'Fc_m7$$\"+3<>z8Fc_m$\"+K>QphFc_m7%7$$\"+$=]eW\"Fc_m$\"+aEvylF c_m7$$\"+bm))[9Fc_m$\"+/j#G0'Fc_m7$$\"+f.4e9Fc_m$\"+#4B#phFc_m7%7$$\"+ tf([_\"Fc_m$\"+dAxylFc_m7$$\"+,cvF:Fc_m$\"+,n!G0'Fc_m7$$\"+(*R*p`\"Fc_ m$\"+u73phFc_m7%7$$\"+kS*Qg\"Fc_m$\"+V!*yylFc_m7$$\"+YAj1;Fc_m$\"+:**y _gFc_m7$$\"+'*=!fh\"Fc_m$\"+&)Q&*ohFc_m7%7$$\"+Ob!Ho\"Fc_m$\"+FN!)ylFc _m7$$\"+5b^&o\"Fc_m$\"+Kax_gFc_m7$$\"+hM\"[p\"Fc_m$\"+L)Q)ohFc_m7%7$$ \"+x7\">w\"Fc_m$\"+6h\")ylFc_m7$$\"+0XSk>Fc_m$\"+)yO)ylF c_m7$$\"+po>A>Fc_m$\"+q@u_gFc_m7$$\"+sccJ>Fc_m$\"+n?bohFc_m7%7$$\"+%)3 !*)*>Fc_m$\"+T`%)ylFc_m7$$\"+1\"*4,?Fc_m$\"+ZohFc_m7%7$$\"+2Cpi\\Fb\\m$\"+#=&3/rFc_m7$$\"+$f2t.&Fb\\m$\"+c`7 !e'Fc_m7$$\"+*R&R>^Fb\\m$\"+=Ry*p'Fc_m7%7$$\"+do@ddFb\\m$\"+XIQ/rFc_m7 $$\"+60t@eFb\\m$\"+$\\F)zlFc_m7$$\"+hq61fFb\\m$\"+RKx)p'Fc_m7%7$$\"+a* R0b'Fb\\m$\"+H3e/rFc_m7$$\"+#yatg'Fb\\m$\"+5(H'zlFc_m7$$\"+YB[$p'Fb\\m $\"+I&>!)p'Fc_m7%7$$\"+fR/VtFb\\m$\"+\"y=Z5(Fc_m7$$\"+X\")z$R(Fb\\m$\" +d<\\zlFc_m7$$\"+3'*G\"[(Fb\\m$\"+fiV(p'Fc_m7%7$$\"+hZ'\\8)Fb\\m$\"+$z =[5(Fc_m7$$\"+6Z#3=)Fb\\m$\"+X.0rFc_m7$$\"+zLBL6Fc_m$\"+8'y\"zlFc_m7$ $\"+QnPU6Fc_m$\"+#e'y&p'Fc_m7%7$$\"+4'z*37Fc_m$\"+q510rFc_m7$$\"+@I277 Fc_m$\"+o%\\\"zlFc_m7$$\"+?TE@7Fc_m$\"+80f&p'Fc_m7%7$$\"+T:-)G\"Fc_m$ \"+M]30rFc_m7$$\"+De#4H\"Fc_m$\"+/b7zlFc_m7$$\"+q(e,I\"Fc_m$\"+>$>ap'F c_m7%7$$\"+$e_qO\"Fc_m$\"+x\\50rFc_m7$$\"+>&*yp8Fc_m$\"+hb5zlFc_m7$$\" +W%f!z8Fc_m$\"+c&o_p'Fc_m7%7$$\"+7X2Y9Fc_m$\"+\\<70rFc_m7$$\"+EBm[9Fc_ m$\"+*y)3zlFc_m7$$\"+m^'zX\"Fc_m$\"+yZ8&p'Fc_m7%7$$\"+S()3D:Fc_m$\"+!* f80rFc_m7$$\"+MGaF:Fc_m$\"+[X2zlFc_m7$$\"+f^(o`\"Fc_m$\"+q_,&p'Fc_m7%7 $$\"++k4/;Fc_m$\"+$=[^5(Fc_m7$$\"+5*Hkg\"Fc_m$\"+bB1zlFc_m7$$\"++))y:; Fc_m$\"+py!\\p'Fc_m7%7$$\"+:%)4$o\"Fc_m$\"+/(e^5(Fc_m7$$\"+JEK&o\"Fc_m $\"+M=0zlFc_m7$$\"+ybq%p\"Fc_m$\"+D3\"[p'Fc_m7%7$$\"+Ub4iFc_m$\"+iG=0rFc_m7$$\"+:x-A>Fc_m$\"+ww-zlFc_m7 $$\"+**3ZJ>Fc_m$\"+i(oXp'Fc_m7%7$$\"+vL1**>Fc_m$\"+u!*=0rFc_m7$$\"+:m$ 4+#Fc_m$\"+k9-zlFc_m7$$\"+*o'R5?Fc_m$\"+E6]%p'Fc_m7%7$$\"+)z%zn\\Fb\\m $\"+b;qIwFc_m7$$\"+-_?K]Fb\\m$\"+j/91rFc_m7$$\"+k^h;^Fb\\m$\"+E)y]A(Fc _m7%7$$\"+YljhdFb\\m$\"+tP#4j(Fc_m7$$\"+A3J\\6Q\")Fb\\m$\"+l$[7j(Fc_m7$$\"+`Xnx\")Fb\\m$\"+`Pf0rFc_m7$$\"+\" ))pwE)Fb\\m$\"+^zpAsFc_m7%7$$\"+h+LH*)Fb\\m$\"+VSIJwFc_m7$$\"+znSl*)Fb \\m$\"+v!Qb5(Fc_m7$$\"+fq47Fc_m$\"+f'G9j (Fc_m7$$\"+<-'=@\"Fc_m$\"+fMT0rFc_m7$$\"+0a9@7Fc_m$\"+hA_@sFc_m7%7$$\" +k8A)G\"Fc_m$\"+'[Y9j(Fc_m7$$\"+-gs!H\"Fc_m$\"+KcR0rFc_m7$$\"+&=Z+I\"F c_m$\"+#=w8A(Fc_m7%7$$\"+94Cn8Fc_m$\"+?8YJwFc_m7$$\"+)=,'p8Fc_m$\"+)z! Q0rFc_m7$$\"+%=a*y8Fc_m$\"+nuC@sFc_m7%7$$\"++EDY9Fc_m$\"+&zt9j(Fc_m7$$ \"+QU[[9Fc_m$\"+B$o`5(Fc_m7$$\"+_b'yX\"Fc_m$\"+(>L6A(Fc_m7%7$$\"+TwDD: Fc_m$\"+(Q%[JwFc_m7$$\"+LRPF:Fc_m$\"+JxN0rFc_m7$$\"+<1yO:Fc_m$\"+r5.@s Fc_m7%7$$\"+9qD/;Fc_m$\"+bM\\JwFc_m7$$\"+'Hpig\"Fc_m$\"+j'[`5(Fc_m7$$ \"+R))p:;Fc_m$\"+a#R4A(Fc_m7%7$$\"+;:D$o\"Fc_m$\"+z7]JwFc_m7$$\"+I&p^o \"Fc_m$\"+R3M0rFc_m7$$\"+w(>Yp\"Fc_m$\"+hi&3A(Fc_m7%7$$\"+,=CiFc_m$\"+X#>:j(Fc_m7$$\"+eM*=#>Fc_m$\" +tGK0rFc_m7$$\"+]bRJ>Fc_m$\"+9\"\\1A(Fc_m7%7$$\"+TB>**>Fc_m$\"+lQ_JwFc _m7$$\"+\\w!3+#Fc_m$\"+a#=`5(Fc_m7$$\"+!GC.,#Fc_m$\"+,7f?sFc_m7%7$$\"+ YJ#>(\\Fb\\m$\"+;#Gs:)Fc_m7$$\"+ao2G]Fb\\m$\"+#[XAj(Fc_m7$$\"+#[`V6&Fb \\m$\"+aqe]xFc_m7%7$$\"+*))4_w&Fb\\m$\"+ArRd\")Fc_m7$$\"+zut8eFb\\m$\" +wl2KwFc_m7$$\"+]&Gj(Fc_m7$$\"+K&)f*o'Fb\\m$\"+1&3$\\xFc_m7 %7$$\"+XGM\\tFb\\m$\"+0sed\")Fc_m7$$\"+f#*\\(Q(Fb\\m$\"+$\\')=j(Fc_m7$ $\"+Oq!yZ(Fb\\m$\"+PP))[xFc_m7%7$$\"+*4f19)Fb\\m$\"+nPkd\")Fc_m7$$\"+t .8v\")Fb\\m$\"+J*H=j(Fc_m7$$\"+=sDm#)Fb\\m$\"+sXa[xFc_m7%7$$\"+Z5lJ*)F b\\m$\"+`god\")Fc_m7$$\"+$z&3j*)Fb\\m$\"+XwyJwFc_m7$$\"+Af)[0*Fb\\m$\" +`vE[xFc_m7%7$$\"+JtRA(*Fb\\m$\"+!\\=x:)Fc_m7$$\"+xoG^(*Fb\\m$\"+3_vJw Fc_m7$$\"+A-lV)*Fb\\m$\"+hq.[xFc_m7%7$$\"+3`H^5Fc_m$\"+:Rud\")Fc_m7$$ \"+]y'R0\"Fc_m$\"+$yHDj5Fc_m$\"+,B%yu(Fc_m7%7$$\"+4eLI 6Fc_m$\"+7Uwd\")Fc_m7$$\"+&3AG8\"Fc_m$\"+([4\\%p8Fc_m$\"+L#o;j(Fc_m7$$\"+n!p)y8Fc_m$\"+ aQHZxFc_m7%7$$\"+BjRY9Fc_m$\"+M\\\"y:)Fc_m7$$\"+:0M[9Fc_m$\"+k(e;j(Fc_ m7$$\"+8]yd9Fc_m$\"+w]>ZxFc_m7%7$$\"+WRRD:Fc_m$\"+uH#y:)Fc_m7$$\"+IwBF :Fc_m$\"+D2lJwFc_m7$$\"+!>/n`\"Fc_m$\"+kn5ZxFc_m7%7$$\"+EmQ/;Fc_m$\"+d )Hy:)Fc_m7$$\"+%oRhg\"Fc_m$\"+TQkJwFc_m7$$\"+Bhi:;Fc_m$\"+Qt-ZxFc_m7%7 $$\"+i]P$o\"Fc_m$\"+&zNy:)Fc_m7$$\"+%)f/&o\"Fc_m$\"+.zjJwFc_m7$$\"+H/b %p\"Fc_m$\"+Cb&pu(Fc_m7%7$$\"+B)fBw\"Fc_m$\"+b4%y:)Fc_m7$$\"+ff&Rw\"Fc _m$\"+VFjJwFc_m7$$\"+*ywMx\"Fc_m$\"+w-*ou(Fc_m7%7$$\"+\"QT8%=Fc_m$\"+l a%y:)Fc_m7$$\"+P\"pG%=Fc_m$\"+L#G;j(Fc_m7$$\"+T\\S_=Fc_m$\"+O2$ou(Fc_m 7%7$$\"+I,K?>Fc_m$\"+J%\\y:)Fc_m7$$\"+C^y@>Fc_m$\"+nUiJwFc_m7$$\"+lYLJ >Fc_m$\"+&=wnu(Fc_m7%7$$\"+.kH**>Fc_m$\"+PH&y:)Fc_m7$$\"+(e.2+#Fc_m$\" +h2iJwFc_m7$$\"+wdE5?Fc_m$\"+AgsYxFc_m7%7$$\"+i)3`(\\Fb\\m$\"+7_p$o)Fc _m7$$\"+Q6pC]Fb\\m$\"+m+Te\")Fc_m7$$\"+F0\\7^Fb\\m$\"+EGDw#)Fc_m7%7$$ \"+5*Q\"odFb\\m$\"+&)e#Qo)Fc_m7$$\"+e%33\"eFb\\m$\"+$Rz#e\")Fc_m7$$\"+ (>5,!fFb\\m$\"+U$>cF)Fc_m7%7$$\"+yl;glFb\\m$\"+9D\"Ro)Fc_m7$$\"+e\"Gxf 'Fb\\m$\"+kF>e\")Fc_m7$$\"+!Ho\")o'Fb\\m$\"+hX9v#)Fc_m7%7$$\"+R'[;N(Fb \\m$\"+tG(Ro)Fc_m7$$\"+lM>&Q(Fb\\m$\"+1C8e\")Fc_m7$$\"+&)e_wuFb\\m$\"+ 4cxu#)Fc_m7%7$$\"+SHuU\")Fb\\m$\"+(f;So)Fc_m7$$\"+Kl/t\")Fb\\m$\"+\"o) 3e\")Fc_m7$$\"+'4(4l#)Fb\\m$\"+92[u#)Fc_m7%7$$\"+I=bL*)Fb\\m$\"+#G\\So )Fc_m7$$\"+5]=h*)Fb\\m$\"+(*f0e\")Fc_m7$$\"+#*f#Q0*Fb\\m$\"+\\'RUF)Fc_ m7%7$$\"+oX9C(*Fb\\m$\"+^V2%o)Fc_m7$$\"+S'R&\\(*Fb\\m$\"+F4.e\")Fc_m7$ $\"+)euE%)*Fb\\m$\"+D*QSF)Fc_m7%7$$\"+ppX^5Fc_m$\"+**R4%o)Fc_m7$$\"+*= 1Q0\"Fc_m$\"+z7,e\")Fc_m7$$\"+>;;j5Fc_m$\"+7#pQF)Fc_m7%7$$\"+Ai[I6Fc_m $\"+%o4To)Fc_m7$$\"+s;nK6Fc_m$\"+%f&*z:)Fc_m7$$\"+ZJ1U6Fc_m$\"+XQst#)F c_m7%7$$\"+0[]47Fc_m$\"+.C7%o)Fc_m7$$\"+Dya67Fc_m$\"+vG)z:)Fc_m7$$\"+9 1(4A\"Fc_m$\"+Tzft#)Fc_m7%7$$\"+wY^)G\"Fc_m$\"+fG8%o)Fc_m7$$\"+!pK/H\" Fc_m$\"+>C(z:)Fc_m7$$\"+OH))*H\"Fc_m$\"+Ty[t#)Fc_m7%7$$\"+Ut^n8Fc_m$\" +g:9%o)Fc_m7$$\"+gZKp8Fc_m$\"+=P'z:)Fc_m7$$\"+x#*zy8Fc_m$\"+X2Rt#)Fc_m 7%7$$\"+zR^Y9Fc_m$\"+x)[To)Fc_m7$$\"+fGA[9Fc_m$\"+,k&z:)Fc_m7$$\"+&)*= xX\"Fc_m$\"+![/LF)Fc_m7%7$$\"+Bb]D:Fc_m$\"+)3bTo)Fc_m7$$\"+^g7F:Fc_m$ \"+!>]z:)Fc_m7$$\"+Q:kO:Fc_m$\"+KtAt#)Fc_m7%7$$\"+DF\\/;Fc_m$\"+1/;%o) Fc_m7$$\"+&eLgg\"Fc_m$\"+s[%z:)Fc_m7$$\"+?lc:;Fc_m$\"+Gz:t#)Fc_m7%7$$ \"+%>wMo\"Fc_m$\"+%*\\;%o)Fc_m7$$\"+_[%\\o\"Fc_m$\"+%GSz:)Fc_m7$$\"+\" f$\\%p\"Fc_m$\"+e^4t#)Fc_m7%7$$\"+KkXiFc_m$\"+Hb<%o)Fc_m7$$\"+[kp@>Fc_m$\"+\\(Hz:)Fc_m7$$\"+uZ GJ>Fc_m$\"+Q$QHF)Fc_m7%7$$\"+\"e\"Q**>Fc_m$\"+P#yTo)Fc_m7$$\"+4%=1+#Fc _m$\"+Tq#z:)Fc_m7$$\"+Qy@5?Fc_m$\"+dW*GF)Fc_m7%7$$\"+Y!>\"y\\Fb\\m$\"+ 8<75#*Fc_m7$$\"+a4)=-&Fb\\m$\"+X^h%o)Fc_m7$$\"+/(Q46&Fb\\m$\"+![P?!))F c_m7%7$$\"+9\"p0x&Fb\\m$\"+hVA5#*Fc_m7$$\"+a#y$3eFb\\m$\"+(\\7Xo)Fc_m7 $$\"+5Lw)*eFb\\m$\"+;K[,))Fc_m7%7$$\"+TqIilFb\\m$\"+$R#H5#*Fc_m7$$\"+& p(e&f'Fb\\m$\"+lWW%o)Fc_m7$$\"+3(ypo'Fb\\m$\"+ps1,))Fc_m7%7$$\"+R4c`tF b\\m$\"+&yR.@*Fc_m7$$\"+l6G$Q(Fb\\m$\"+tqR%o)Fc_m7$$\"+13YvuFb\\m$\"+' pV2!))Fc_m7%7$$\"+Y4ZW\")Fb\\m$\"+8TP5#*Fc_m7$$\"+E&=8<)Fb\\m$\"+YFO%o )Fc_m7$$\"+')H8k#)Fb\\m$\"+Y[[+))Fc_m7%7$$\"+))y7N*)Fb\\m$\"+q(*R5#*Fc _m7$$\"+_*3'f*)Fb\\m$\"+)3PVo)Fc_m7$$\"+*RXH0*Fb\\m$\"+)3t-!))Fc_m7%7$ $\"+1KfD(*Fb\\m$\"+[%>/@*Fc_m7$$\"+-54[(*Fb\\m$\"+5uJ%o)Fc_m7$$\"+>U'= %)*Fb\\m$\"+fm4+))Fc_m7%7$$\"+&*4f^5Fc_m$\"+q[V5#*Fc_m7$$\"+j@n`5Fc_m$ \"+))>I%o)Fc_m7$$\"+ol3j5Fc_m$\"+0u%**z)Fc_m7%7$$\"+<4hI6Fc_m$\"+!=Z/@ *Fc_m7$$\"+xpaK6Fc_m$\"+y'*G%o)Fc_m7$$\"+hK*>9\"Fc_m$\"+.&>)*z)Fc_m7%7 $$\"+$Q@'47Fc_m$\"+jrX5#*Fc_m7$$\"+Z7V67Fc_m$\"+&pzUo)Fc_m7$$\"+F_!4A \"Fc_m$\"+z'3(*z)Fc_m7%7$$\"+GTi)G\"Fc_m$\"+p`Y5#*Fc_m7$$\"+QKK!H\"Fc_ m$\"+*[rUo)Fc_m7$$\"+0:#)*H\"Fc_m$\"+Js/@*Fc_m7$$\"+9;Ap8Fc_m$\"+gYE%o)Fc_m7$$\"+^8uy8Fc_m$\"+0i_*z)Fc_m7% 7$$\"+2:hY9Fc_m$\"+SzZ5#*Fc_m7$$\"+J`7[9Fc_m$\"+=*eUo)Fc_m7$$\"+&=kwX \"Fc_m$\"+*>]%*z)Fc_m7%7$$\"+7!)fD:Fc_m$\"+:G[5#*Fc_m7$$\"+iN.F:Fc_m$ \"+WSD%o)Fc_m7$$\"+Y&*eO:Fc_m$\"+2AQ*z)Fc_m7%7$$\"+q1e/;Fc_m$\"+))p[5# *Fc_m7$$\"+Sc%fg\"Fc_m$\"+q)\\Uo)Fc_m7$$\"+hq^:;Fc_m$\"+C5K*z)Fc_m7%7$ $\"+?+c$o\"Fc_m$\"+*e!\\5#*Fc_m7$$\"+E5'[o\"Fc_m$\"+qiC%o)Fc_m7$$\"+Jk W%p\"Fc_m$\"+zcE*z)Fc_m7%7$$\"+3l`iFc_m$\"+b))\\5#*Fc_m7$$\"+\\Hi@>Fc_m$\"+.!QUo)Fc_m7$$\"+$Q V7$>Fc_m$\"+ct7*z)Fc_m7%7$$\"+#=_%**>Fc_m$\"+\")4]5#*Fc_m7$$\"+3ya+?Fc _m$\"+xeB%o)Fc_m7$$\"+p!y,,#Fc_m$\"+P')3*z)Fc_m7%7$$\"+)fw/)\\Fb\\m$\" +Y+_O(*Fc_m7$$\"+-M_>]Fb\\m$\"+$R[3@*Fc_m7$$\"+cHj4^Fb\\m$\"+XN\"zK*Fc _m7%7$$\"+@tgsdFb\\m$\"+\"y,mt*Fc_m7$$\"+Z+M1eFb\\m$\"+dmw5#*Fc_m7$$\" +$yIw*eFb\\m$\"+iVUF$*Fc_m7%7$$\"+6>5klFb\\m$\"+VflO(*Fc_m7$$\"+DGz$f' Fb\\m$\"+&\\72@*Fc_m7$$\"+]*yfo'Fb\\m$\"+No0F$*Fc_m7%7$$\"+yU;btFb\\m$ \"+oOpO(*Fc_m7$$\"+Eyn\"Q(Fb\\m$\"+rZn5#*Fc_m7$$\"+=gcuuFb\\m$\"+l1xE$ *Fc_m7%7$$\"+K'>f9)Fb\\m$\"+!*4sO(*Fc_m7$$\"+S)p)p\")Fb\\m$\"+[uk5#*Fc _m7$$\"+dKKj#)Fb\\m$\"+i:aE$*Fc_m7%7$$\"+&4\\k$*)Fb\\m$\"+59uO(*Fc_m7$ $\"+XxGe*)Fb\\m$\"+Gqi5#*Fc_m7$$\"+&)f?_!*Fb\\m$\"+@SNE$*Fc_m7%7$$\"+K v!os*Fb\\m$\"+rqvO(*Fc_m7$$\"+wm(ou*Fb\\m$\"+n8h5#*Fc_m7$$\"+)*Q=T)*Fb \\m$\"+#o(>E$*Fc_m7%7$$\"+QLq^5Fc_m$\"+W$pnt*Fc_m7$$\"+?)fN0\"Fc_m$\"+ %4*f5#*Fc_m7$$\"+sN-j5Fc_m$\"+j`1E$*Fc_m7%7$$\"+NarI6Fc_m$\"+S\"znt*Fc _m7$$\"+fCWK6Fc_m$\"+)H*e5#*Fc_m7$$\"+2Y$>9\"Fc_m$\"+G>&fK*Fc_m7%7$$\" +%4>(47Fc_m$\"+%3(yO(*Fc_m7$$\"+ONL67Fc_m$\"+b8e5#*Fc_m7$$\"+d.&3A\"Fc _m$\"+0O&eK*Fc_m7%7$$\"+ler)G\"Fc_m$\"+9OzO(*Fc_m7$$\"+,:B!H\"Fc_m$\"+ C[d5#*Fc_m7$$\"+f*p(*H\"Fc_m$\"+kvwD$*Fc_m7%7$$\"+Rpqn8Fc_m$\"+Z!*zO(* Fc_m7$$\"+j^8p8Fc_m$\"+\"Rp0@*Fc_m7$$\"+\\Fpy8Fc_m$\"+T;pD$*Fc_m7%7$$ \"+ZKpY9Fc_m$\"+;O!ot*Fc_m7$$\"+\"fV![9Fc_m$\"+A[c5#*Fc_m7$$\"+5#=wX\" Fc_m$\"+^TiD$*Fc_m7%7$$\"+GbnD:Fc_m$\"+&\\2ot*Fc_m7$$\"+Yg&p_\"Fc_m$\" +V4c5#*Fc_m7$$\"+GfaO:Fc_m$\"+iPcD$*Fc_m7%7$$\"+wVl/;Fc_m$\"+;3\"ot*Fc _m7$$\"+M>(eg\"Fc_m$\"+Awb5#*Fc_m7$$\"+sbZ:;Fc_m$\"+7%4bK*Fc_m7%7$$\"+ u-j$o\"Fc_m$\"+\"o8ot*Fc_m7$$\"+s2z%o\"Fc_m$\"+dZb5#*Fc_m7$$\"+soS%p\" Fc_m$\"+P-YD$*Fc_m7%7$$\"+>OgiFc_m$\"+f-#ot*Fc_m7$$\"+^8c@>Fc_m$\"+z\"[0@*Fc_m7$$\"+p'37$>Fc_m$ \"+*HP`K*Fc_m7%7$$\"+\\8^**>Fc_m$\"+]>#ot*Fc_m7$$\"+T')[+?Fc_m$\"+)[Y0 @*Fc_m7$$\"+;Z95?Fc_m$\"+xGID$*Fc_m7%7$$\"+UMZ#)\\Fb\\m$\"+Q)*GE5Ff[m7 $$\"+el_<]Fb\\m$\"+S;5P(*Fc_m7$$\"+DU_3^Fb\\m$\"+n5'Q&)*Fc_m7%7$$\"+=L LudFb\\m$\"+EkHE5Ff[m7$$\"+]Sh/eFb\\m$\"+fd.P(*Fc_m7$$\"+t'pm*eFb\\m$ \"+9gU`)*Fc_m7%7$$\"+M;illFb\\m$\"+\"z+j-\"Ff[m7$$\"+-JF#f'Fb\\m$\"+5@ *pt*Fc_m7$$\"+`38&o'Fb\\m$\"+F))4`)*Fc_m7%7$$\"++<_ctFb\\m$\"+JQIE5Ff[ m7$$\"+//K!Q(Fb\\m$\"+6<'pt*Fc_m7$$\"+'>2QZ(Fb\\m$\"+hQ%G&)*Fc_m7%7$$ \"+Ng9Z\")Fb\\m$\"+KgIE5Ff[m7$$\"+PMko\")Fb\\m$\"+'pRpt*Fc_m7$$\"+Jnji #)Fb\\m$\"+/'RE&)*Fc_m7%7$$\"+@vcP*)Fb\\m$\"+ywIE5Ff[m7$$\"+>$pr&*)Fb \\m$\"+VK#pt*Fc_m7$$\"+$>z:0*Fb\\m$\"+3BZ_)*Fc_m7%7$$\"+Sa$ys*Fb\\m$\" +R*3j-\"Ff[m7$$\"+o([eu*Fb\\m$\"+D1\"pt*Fc_m7$$\"+(G21%)*Fb\\m$\"+\"yK B&)*Fc_m7%7$$\"+J%)z^5Fc_m$\"+G*4j-\"Ff[m7$$\"+FZY`5Fc_m$\"+Q2!pt*Fc_m 7$$\"+'=qH1\"Fc_m$\"+WY@_)*Fc_m7%7$$\"+.R!38\"Fc_m$\"+<2JE5Ff[m7$$\"+ \"*RNK6Fc_m$\"+XG*ot*Fc_m7$$\"+1\\)=9\"Fc_m$\"+IL6_)*Fc_m7%7$$\"+*z,)4 7Fc_m$\"+d8JE5Ff[m7$$\"+J3D67Fc_m$\"+Yk)ot*Fc_m7$$\"+lQ!3A\"Fc_m$\"+([ D?&)*Fc_m7%7$$\"+7Nz)G\"Fc_m$\"+%)=JE5Ff[m7$$\"+aQ:!H\"Fc_m$\"+&=\")ot *Fc_m7$$\"+(GE(*H\"Fc_m$\"+(f[>&)*Fc_m7%7$$\"+5,yn8Fc_m$\"+@BJE5Ff[m7$ $\"+#*>1p8Fc_m$\"+3o(ot*Fc_m7$$\"+w:ly8Fc_m$\"+K2)=&)*Fc_m7%7$$\"+ICwY 9Fc_m$\"+*o7j-\"Ff[m7$$\"+3W(zW\"Fc_m$\"+FJ(ot*Fc_m7$$\"+l#zvX\"Fc_m$ \"+#R?=&)*Fc_m7%7$$\"+N6uD:Fc_m$\"+-IJE5Ff[m7$$\"+R/*o_\"Fc_m$\"+.+(ot *Fc_m7$$\"+$)*3l`\"Fc_m$\"+\"Rm<&)*Fc_m7%7$$\"+fnr/;Fc_m$\"+pKJE5Ff[m7 $$\"+^&4eg\"Fc_m$\"+Ft'ot*Fc_m7$$\"+I/W:;Fc_m$\"+\"y<<&)*Fc_m7%7$$\"+N (*o$o\"Fc_m$\"++NJE5Ff[m7$$\"+68t%o\"Fc_m$\"+>]'ot*Fc_m7$$\"+lLP%p\"Fc _m$\"+#zt;&)*Fc_m7%7$$\"+=/miFc_m$\"+ISJE5Ff[m7$$\"+<#4:#>Fc_m$\"+?(fot*Fc_m7$$\"+o#z6$>Fc_m$\"+#z j:&)*Fc_m7%7$$\"+E9c**>Fc_m$\"+mTJE5Ff[m7$$\"+k&Q/+#Fc_m$\"+e$eot*Fc_m 7$$\"+qk65?Fc_m$\"+&)H`^)*Fc_m-Fa[m6&Fc[m$\")THNiFf[mFdael$\")-\\DPFf[ m-%+AXESLABELSG6$%\"xG%\"yG-%%VIEWG6$;$\"++++]UFb\\m$\"++++v?Fc_m;$!++ +++]Fb\\m$\"++++]5Ff[m" 2 600 362 362 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 25965 29806 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 507 15 "Second example:" }}{PARA 0 "" 0 "" {TEXT -1 46 "(Edwards and Penney, Section 1.6, Exercise 21)" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "diff_eq := diff(y(x),x) \+ - y(x) = y(x)^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(diff_eqG/,&-%%d iffG6$-%\"yG6#%\"xGF-\"\"\"F*!\"\"*$F*\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Bernoulli_ode(diff_eq);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7,/,&-%%diffG6$-%\"yG6#%\"xGF,\"\"\"F)!\"\"*$F)\"\"$/-% %zetaGF+*$F)!\"#/,&-F'6$F2F,F-F2\"\"#F5/*&-%$expG6#-%$IntG6$F:F,F-F7F- ,$F=F5/-%%DiffG6$**%\"(GF-F=F-F2F-%\")GF-F,FC/*&F=F-F2F-,&-FA6$FCF,F-% #_CGF-/*&-F>6#,$F,F:F-F2F-,&-FA6$,$FSF5F,F-FPF-/FR,&FSF.FPF-/F2*&-F>6# ,$F,F5F-FenF-/F4Fgn" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 34 "Again let's plot a solution curve:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "dfplot := df ieldplot(diff_eq, y(x), x = 1/2 .. 1.2, y = 0 ..10, color = gray):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "soln_plot := implicitplot( 1/y^2 = exp(-2*x)*(-exp(2*x)+10), x = 1/2 .. 1.2, y = 1/2 ..10, color \+ = magenta, thickness=2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display(\{dfplot, soln_plot\});" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CU RVESG6^q7$7$$\"1+++++++]!#;$\"1G^,0u^`oF*7$$\"1]e'p2ZN8&F*$\"1.\\.%Qvv )pF*7$7$$\"1++++++!G&F*$\"1(o[@e)eMrF*F-7$F37$$\"1uq?NJp%R&F*$\"10S!zI ]MC(F*7$7$$\"1++++++gbF*$\"1[#*4!Q_.S(F*F97$F?7$$\"1(3(yZ\\tccF*$\"1(p Ydcor[(F*7$7$$\"1,+++++SeF*$\"1rV'>XU;l(F*FE7$FK7$$\"1!Q%4bjj>fF*$\"16 x9&*3A>xF*7$7$$\"1,+++++?hF*$\"1dNP\\qC*)yF*FQ7$FW7$$\"1/RL4?O$='F*$\" 1UF=;q3SzF*7$7$$\"1,++++++kF*$\"1B94&\\6R6)F*Fgn7$F]o7$$\"1Lh*yUxyW'F* $\"1VR72\\B]\")F*7$7$$\"1,+++++!o'F*$\"1)yg4_SjK)F*Fco7$7$Fjo$\"1*yg4_ SjK)F*7$$\"1[:%o.\\Jr'F*$\"1)G$H9-7]$)F*7$7$$\"1-+++++gpF*$\"1Z$>&y/?F &)F*Fbp7$7$Fip$\"1[$>&y/?F&)F*7$$\"155N0U9zpF*$\"1P?_%y&=S&)F*7$7$$\"1 -+++++SsF*$\"1\\UAH97<()F*Faq7$7$Fhq$\"1[UAH97<()F*7$$\"1xG'>FJeC(F*$ \"1j_248'3s)F*7$7$$\"1.@Q/aAptF*$\"1+++++++))F*F`r7$Ffr7$$\"13:@IEb&\\ (F*$\"1PQ%Gt&yJ\"*F*7$7$$\"1-+++++?vF*$\"1pT%oG%*f>*F*F\\s7$7$$\"1.+++ ++?vF*Fes7$$\"1rvv\"GC?t(F*$\"15(=ZgFDs*F*7$7$$\"1-++++++yF*$\"1mM+3gL \"*)*F*F[t7$7$$\"1,++++++yF*Fdt7$$\"1MP3 \"F_u7$7$$\"1.+++++g$)F*$\"1')z44v/<6F_uFgu7$F]v7$$\"1!Rq!*\\A7X)F*$\" 1.f(p.)>O6F_u7$7$$\"1.+++++S')F*$\"15y8)[Ge<\"F_uFcv7$Fiv7$$\"1$>eiD2T p)F*$\"1*f\\Osol=\"F_u7$7$$\"1.+++++?*)F*$\"1=fE/#39B\"F_uF_w7$Few7$$ \"1#fkh.3&Q*)F*$\"1'[>4&>)[B\"F_u7$7$$\"1pSxzjLs!*F*$\"1++++++g7F_uF[x 7$Fax7$$\"15SM%f\"fm\"*F*$\"1hX5z*R`I\"F_u7$7$$\"1/++++++#*F*$\"1%pfQc 59K\"F_uFgx7$F]y7$$\"1\"4FX(R#eP*F*$\"1(4c)[j)p%)fw,\"F_u$\"1A&GBO;Y$=F_u7$7$$\"1++++++K5F_u$\"1?R ]VD!p%>F_uFf\\l7$F\\]l7$$\"14ub\\\\[N5F_u$\"1+m+cUqs>F_u7$7$$\"1Y\"[[- t=/\"F_u$\"1++++++??F_uFb]l7$Fh]l7$$\"1[ZI\\l3^5F_u$\"1pbVf#o49#F_u7$7 $$\"1++++++g5F_u$\"1#pUNs'*zD#F_uF^^l7$Fd^l7$$\"1(eOlkka1\"F_u$\"121') Rp$eK#F_u7$7$$\"1$3e!4'Q92\"F_u$\"1+++++++CF_uFj^l7$F`_l7$$\"164$)>57y 5F_u$\"1mLst=2MDF_u7$7$$\"1,+++++)3\"F_u$\"1sfs%zxAt#F_uFf_l7$F\\`l7$$ \"10OItkY*3\"F_u$\"1A#3B'y4gFF_u7$7$$\"1tMXqb^!4\"F_u$\"1++++++!y#F_uF b`l7$7$Fi`l$\"1************zFF_u7$$\"1>9eL8q)4\"F_u$\"1b2o:ww9IF_u7$7$ $\"1@exD_w.6F_u$\"1++++++gJF_uFaal7$Fgal7$$\"1XQMl^z16F_u$\"1Ey/cF#\\G $F_u7$7$$\"1fXaP>)H6\"F_u$\"1++++++SNF_uF]bl7$7$$\"1gXaP>)H6\"F_uFfbl7 $$\"1LC4yCc86F_u$\"1Z)fWl!3tNF_u7$7$$\"1,+++++;6F_u$\"1%)\\&yvw>r$F_uF \\cl7$Fbcl7$$\"1.[8#3%3>6F_u$\"1>\"*f*fW\"yQF_u7$7$$\"1Su7?4')>6F_u$\" 1************>RF_uFhcl7$F^dl7$$\"10V%F_u7$7$$\"1z YTUz7D6F_u$\"1+++++++VF_uFddl7$Fjdl7$$\"1kwRzf]F6F_u$\"1*GgCUZQ_%F_u7$ 7$$\"1ZK/i[;H6F_u$\"1++++++!o%F_uF`el7$Ffel7$$\"1EGf+-nI6F_u$\"1af_?W! 4'[F_u7$7$$\"1Z436pKK6F_u$\"1************f]F_uF\\fl7$7$Fcfl$\"1++++++g ]F_u7$$\"11p&pu\"HL6F_u$\"1T\"*H\"HE`?&F_u7$7$$\"1(QI$p(\\[8\"F_u$\"1+ +++++SaF_uF[gl7$Fagl7$$\"18/y!esa8\"F_u$\"1ps$3EHdb&F_u7$7$$\"1a4s'y%* o8\"F_u$\"1************>eF_uFggl7$F]hl7$$\"1tZf:rHP6F_u$\"1*4Gprn4\"fF _u7$7$$\"1]\\ePadQ6F_u$\"1*************>'F_uFchl7$Fihl7$$\"1qKY$RL)Q6F _u$\"1H*p:B=,F'F_u7$7$$\"1]>H3M(*R6F_u$\"1************zlF_uF_il7$Feil7 $$\"1$>^lhN,9\"F_u$\"19\"[R?XCj'F_u7$7$$\"1zu#Qr[69\"F_u$\"1********** **fpF_uF[jl7$Fajl7$$\"1i%[**zY79\"F_u$\"1>B%y&[O(*pF_u7$7$$\"1Y;4[i9U6 F_u$\"1************RtF_uFgjl7$F][m7$$\"1:\\426?U6F_u$\"1:!pla8WO(F_u7$ 7$$\"1M0bN,+V6F_u$\"1++++++?xF_uFc[m7$7$Fj[m$\"1************>xF_u7$$\" 1=?Jjd-V6F_u$\"1?Ei$y@Kt(F_u7$7$$\"1^l#*)oOP9\"F_u$\"1+++++++\")F_uFb \\m7$Fh\\m7$$\"13F#4dUP9\"F_u$\"1%pM.o$\\.\")F_u7$7$$\"1,+++++W6F_u$\" 1xGE)o'Rc#)F_uF^]m7$Fd]m7$$\"1rz%*\\()QW6F_u$\"1\")*[y5CZZ)F_u7$7$$\"1 r$3T9)RW6F_u$\"1++++++![)F_uFj]m7$F`^m7$$\"1JnR;\"p\\9\"F_u$\"1uV/1x%o %))F_u7$7$$\"1hT+(e*)\\9\"F_u$\"1,+++++g))F_uFf^m7$7$F]_m$\"1.+++++g)) F_u7$$\"1LG>[?[X6F_u$\"1j:\"))['))>#*F_u7$7$$\"1_L5r&4b9\"F_u$\"1-++++ +S#*F_uFe_m7$F[`m7$$\"1M3Iht$f9\"F_u$\"1,()[Rsq$f*F_u7$7$$\"1mR+h\"pf9 \"F_u$\"1.+++++?'*F_uFa`m7$Fg`m7$$\"1)*HT*>Vj9\"F_u$\"1%*y`O%*>o**F_u7 $7$$\"1xL\")ftPY6F_u$\"#5\"\"!F]am-%'COLOURG6&%$RGBG$\"*++++\"!\")Fham F]bm-%*THICKNESSG6#\"\"#-F$6]dl7%7$$\"+u%*y:[!#5Fham7$$\"+E0@%=&FjbmFh am7$$\"+G]W/^Fjbm$\"+tt%*yl!#67%7$$\"+F0@%=&FjbmFham7$$\"+z:j_bFjbmFha m7$$\"+\"3mGZ&FjbmFacm7%7$$\"+!eJEb&FjbmFham7$$\"+KE0@fFjbmFham7$$\"+M rGTeFjbmFacm7%7$$\"+LE0@fFjbmFham7$$\"+&ot%*G'FjbmFham7$$\"+(=3(4iFjbm Facm7%7$$\"+'ot%*G'FjbmFham7$$\"+QZ*yl'FjbmFham7$$\"+S#H\"ylFjbmFacm7% 7$$\"+RZ*yl'FjbmFham7$$\"+\"z:j-(FjbmFham7$$\"+$H]l%pFjbmFacm7%7$$\"+# z:j-(FjbmFham7$$\"+Wot%R(FjbmFham7$$\"+Y8(\\J(FjbmFacm7%7$$\"+Xot%R(Fj bmFham7$$\"+(*y:jxFjbmFham7$$\"+*R#R$o(FjbmFacm7%7$$\"+)*y:jxFjbmFham7 $$\"+]*y:8)FjbmFham7$$\"+_M\"=0)FjbmFacm7%7$$\"+^*y:8)FjbmFham7$$\"+.+ ++&)FjbmFham7$$\"+0XB?%)FjbmFacm7%7$$\"+/+++&)FjbmFham7$$\"+c5Uo))Fjbm Fham7$$\"+ebl)y)FjbmFacm7%7$$\"+d5Uo))FjbmFham7$$\"+4@%oB*FjbmFham7$$ \"+6m2d\"*FjbmFacm7%7$$\"+5@%oB*FjbmFham7$$\"+iJE0'*FjbmFham7$$\"+kw\\ D&*FjbmFacm7%7$$\"+jJE0'*FjbmFham7$$\"+:Uot**FjbmFham7$$\"+<(=R*)*Fjbm Facm7%7$$\"+9Uot**FjbmFham7$$\"+F0@M5!\"*Fham7$$\"+xRBE5F]\\nFacm7%7$$ \"+E0@M5F]\\nFham7$$\"+KE0r5F]\\nFham7$$\"+#3wI1\"F]\\nFacm7%7$$\"+JE0 r5F]\\nFham7$$\"+PZ*y5\"F]\\nFham7$$\"+(==**4\"F]\\nFacm7%7$$\"+OZ*y5 \"F]\\nFham7$$\"+UotW6F]\\nFham7$$\"+#Hgn8\"F]\\nFacm7%7$$\"+TotW6F]\\ nFham7$$\"+Z*y:=\"F]\\nFham7$$\"+(R-O<\"F]\\nFacm7%7$$\"+Y*y:=\"F]\\nF ham7$$\"+_5U=7F]\\nFham7$$\"+-XW57F]\\nFacm7%7$$\"+m!*z:[Fjbm$\"+KDIO_ Fjbm7$$\"+M4?%=&Fjbm$\"+eK,!H&Fjbm7$$\"+@'pR5&Fjbm$\"+B]COfFjbm7%7$$\" +>,A%=&FjbmFg_n7$$\"+()>i_bFjbmF\\`n7$$\"+u1RsaFjbmFa`n7%7$$\"+s6k_bFj bmFg_n7$$\"+SI/@fFjbmF\\`n7$$\"+F<\"3%eFjbmFa`n7%7$$\"+DA1@fFjbmFg_n7$ $\"+$4k%*G'FjbmF\\`n7$$\"+!yK#4iFjbmFa`n7%7$$\"+yK[*G'FjbmFg_n7$$\"+Y^ )yl'FjbmF\\`n7$$\"+LQlxlFjbmFa`n7%7$$\"+JV!zl'FjbmFg_n7$$\"+*>1j-(Fjbm F\\`n7$$\"+')[2YpFjbmFa`n7%7$$\"+%QDj-(FjbmFg_n7$$\"+_ss%R(FjbmF\\`n7$ $\"+Rf\\9tFjbmFa`n7%7$$\"+Pku%R(FjbmFg_n7$$\"+0$[Jw(FjbmF\\`n7$$\"+#*p \"Ho(FjbmFa`n7%7$$\"+!\\nJw(FjbmFg_n7$$\"+e$p:8)FjbmF\\`n7$$\"+X!Q80)F jbmFa`n7%7$$\"+V&)eJ\")FjbmFg_n7$$\"+6/***\\)FjbmF\\`n7$$\"+)4f(>%)Fjb mFa`n7%7$$\"+'f4+])FjbmFg_n7$$\"+k9To))FjbmF\\`n7$$\"+^,=)y)FjbmFa`n7% 7$$\"+\\1Vo))FjbmFg_n7$$\"+PeFjbmF_]o7%7$$\"+RNm@fFjbmFe\\o7$$\" +!yi))G'FjbmFj\\o7$$\"+NVh0iFjbmF_]o7%7$$\"+#f%3!H'FjbmFe\\o7$$\"+LQGd mFjbmFj\\o7$$\"+)QNSd'FjbmF_]o7%7$$\"+Xc]emFjbmFe\\o7$$\"+')[qDqFjbmFj \\o7$$\"+TkXUpFjbmF_]o7%7$$\"+)pEp-(FjbmFe\\o7$$\"+Rf7%R(FjbmFj\\o7$$ \"+%\\x3J(FjbmF_]o7%7$$\"+^xM&R(FjbmFe\\o7$$\"+#*paixFjbmFj\\o7$$\"+Z& )HzwFjbmF_]o7%7$$\"+/)oPw(FjbmFe\\o7$$\"+X!o48)FjbmFj\\o7$$\"++'>x/)Fj bmF_]o7%7$$\"+d)*=K\")FjbmFe\\o7$$\"+)4*Q*\\)FjbmFj\\o7$$\"+`19;%)Fjbm F_]o7%7$$\"+54h+&)FjbmFe\\o7$$\"+^,\"y'))FjbmFj\\o7$$\"+1.p))FjbmFe\\o7$$\"+/7BO#*FjbmFj\\o7$$\"+fF)H:*FjbmF_]o7%7$$ \"+;IXP#*FjbmFe\\o7$$\"+dAl/'*FjbmFj\\o7$$\"+7QS@&*FjbmF_]o7%7$$\"+pS( eg*FjbmFe\\o7$$\"+5L2t**FjbmFj\\o7$$\"+l[#)*))*FjbmF_]o7%7$$\"+?^Hu**F jbmFe\\o7$$\"+O%\\T.\"F]\\nFj\\o7$$\"+#fCe-\"F]\\nF_]o7%7$$\"+<;FM5F] \\nFe\\o7$$\"+T:*42\"F]\\nFj\\o7$$\"+(pmE1\"F]\\nF_]o7%7$$\"+AP6r5F]\\ nFe\\o7$$\"+YO$y5\"F]\\nFj\\o7$$\"+-)3&*4\"F]\\nF_]o7%7$$\"+Fe&z5\"F] \\nFe\\o7$$\"+^dnW6F]\\nFj\\o7$$\"+24NO6F]\\nF_]o7%7$$\"+KzzW6F]\\nFe \\o7$$\"+cy^\"=\"F]\\nFj\\o7$$\"+7I>t6F]\\nF_]o7%7$$\"+P+k\"=\"F]\\nFe \\o7$$\"+h*f$=7F]\\nFj\\o7$$\"+<^.57F]\\nF_]o7%7$$\"+H#3C#[Fjbm$\"+V&R !4:F]\\n7$$\"+rb)[;F]\\n7$$\"+4%e%)3&Fjbm$\"+^)4?o\"F]\\ n7%7$$\"+#GH3>&FjbmFcio7$$\"+CG,YbFjbmFhio7$$\"+i%zoX&FjbmF]jo7%7$$\"+ N.DfbFjbmFcio7$$\"+xQV9fFjbmFhio7$$\"+:0IDeFjbmF]jo7%7$$\"+)Qrw#fFjbmF cio7$$\"+I\\&GG'FjbmFhio7$$\"+o:s$>'FjbmF]jo7%7$$\"+TC4'H'FjbmFcio7$$ \"+$)fF^mFjbmFhio7$$\"+@E9ilFjbmF]jo7%7$$\"+%\\8Xm'FjbmFcio7$$\"+Oqp>q FjbmFhio7$$\"+uOcIpFjbmF]jo7%7$$\"+ZX$H.(FjbmFcio7$$\"+*3=\")Q(FjbmFhi o7$$\"+FZ)*)H(FjbmF]jo7%7$$\"++cN,uFjbmFcio7$$\"+U\"Rlv(FjbmFhio7$$\"+ !y0um(FjbmF]jo7%7$$\"+`mxpxFjbmFcio7$$\"+&>g\\7)FjbmFhio7$$\"+Lo#e.)Fj bmF]jo7%7$$\"+1x>Q\")FjbmFcio7$$\"+[7Q$\\)FjbmFhio7$$\"+')yC/%)FjbmF]j o7%7$$\"+f(=m])FjbmFcio7$$\"+,B!='))FjbmFhio7$$\"+R*oEx)FjbmF]jo7%7$$ \"+7)R]())FjbmFcio7$$\"+aLAI#*FjbmFhio7$$\"+#***3T\"*FjbmF]jo7%7$$\"+l 3YV#*FjbmFcio7$$\"+2Wk)f*FjbmFhio7$$\"+X5^4&*FjbmF]jo7%7$$\"+=>)=h*Fjb mFcio7$$\"+ga1n**FjbmFhio7$$\"+)4Kz()*FjbmF]jo7%7$$\"+pHI!)**FjbmFcio7 $$\"+^'[N.\"F]\\nFhio7$$\"+:`jC5F]\\nF]jo7%7$$\"+-C([.\"F]\\nFcio7$$\" +c2Rq5F]\\nFhio7$$\"+?uZh5F]\\nF]jo7%7$$\"+2Xrr5F]\\nFcio7$$\"+hGB26F] \\nFhio7$$\"+D&>$)4\"F]\\nF]jo7%7$$\"+7mb36F]\\nFcio7$$\"+m\\2W6F]\\nF hio7$$\"+I;;N6F]\\nF]jo7%7$$\"+<()RX6F]\\nFcio7$$\"+rq\"4=\"F]\\nFhio7 $$\"+NP+s6F]\\nF]jo7%7$$\"+A3C#=\"F]\\nFcio7$$\"+w\"fx@\"F]\\nFhio7$$ \"+Se%)37F]\\nF]jo7%7$$\"+$osd%[Fjbm$\"+PmNh>F]\\n7$$\"+C#F]\\n7%7$$\"+OP>9_FjbmFafp7$$ \"+q$[E_&FjbmFffp7$$\"+TBoIaFjbmF[gp7%7$$\"+*y9Ee&FjbmFafp7$$\"+B%p5*e FjbmFffp7$$\"+%R.\"*z&FjbmF[gp7%7$$\"+Ue.^fFjbmFafp7$$\"+w/\\fiFjbmFff p7$$\"+ZW_nhFjbmF[gp7%7$$\"+&*oX>jFjbmFafp7$$\"+H:\"zi'FjbmFffp7$$\"++ b%f`'FjbmF[gp7%7$$\"+[z(yo'FjbmFafp7$$\"+#eKj*pFjbmFffp7$$\"+`lO/pFjbm F[gp7%7$$\"+,!*HcqFjbmFafp7$$\"+NOvktFjbmFffp7$$\"+1wyssFjbmF[gp7%7$$ \"+a+sCuFjbmFafp7$$\"+)ouJt(FjbmFffp7$$\"+f'37k(FjbmF[gp7%7$$\"+269$z( FjbmFafp7$$\"+Tdf,\")FjbmFffp7$$\"+7(H'4!)FjbmF[gp7%7$$\"+g@ch\")FjbmF afp7$$\"+%z;+Z)FjbmFffp7$$\"+l20y$)FjbmF[gp7%7$$\"+8K)*H&)FjbmFafp7$$ \"+ZyVQ))FjbmFffp7$$\"+==ZY()FjbmF[gp7%7$$\"+mUS)*))FjbmFafp7$$\"++*eo ?*FjbmFffp7$$\"+rG*[6*FjbmF[gp7%7$$\"+>`#oE*FjbmFafp7$$\"+`*z_d*FjbmFf fp7$$\"+CRJ$[*FjbmF[gp7%7$$\"+sjCN'*FjbmFafp7$$\"+15qV**FjbmFffp7$$\"+ x\\t^)*FjbmF[gp7%7$$\"+UnO+5F]\\nFafp7$$\"+1A@J5F]\\nFffp7$$\"+.c,A5F] \\nF[gp7%7$$\"+Z)3s.\"F]\\nFafp7$$\"+6V0o5F]\\nFffp7$$\"+3x&)e5F]\\nF[ gp7%7$$\"+_40u5F]\\nFafp7$$\"+;k*[5\"F]\\nFffp7$$\"+8)*p&4\"F]\\nF[gp7 %7$$\"+dI*36\"F]\\nFafp7$$\"+@&Q<9\"F]\\nFffp7$$\"+=>aK6F]\\nF[gp7%7$$ \"+i^tZ6F]\\nFafp7$$\"+E1ey6F]\\nFffp7$$\"+BSQp6F]\\nF[gp7%7$$\"+nsd%= \"F]\\nFafp7$$\"+JFU:7F]\\nFffp7$$\"+GhA17F]\\nF[gp7%7$$\"+]ZN')[Fjbm$ \"+@#pWU#F]\\n7$$\"+]_k8^Fjbm$\"+x')oQGF]\\n7$$\"+67>G]Fjbm$\"+B^f*y#F ]\\n7%7$$\"+.exa_FjbmF_cq7$$\"+.j1#[&FjbmFdcq7$$\"+kAh'R&FjbmFicq7%7$$ \"+co>BcFjbmF_cq7$$\"+ct[]eFjbmFdcq7$$\"+C_u6F]\\nFdcq7$$\"+ :q(f;\"F]\\nFicq7%7$$\"+uaj)=\"F]\\nF_cq7$$\"+CXO67F]\\nFdcq7$$\"+?\"> G?\"F]\\nFicq7%7$$\"+)Q**Q#\\Fjbm$\"+ao)FjbmFg`r7%7$$\"+r4`w*)FjbmF]`r7$$\"+&>K(G\"*FjbmFb `r7$$\"+g0%Q0*FjbmFg`r7%7$$\"+C?&\\M*FjbmF]`r7$$\"+[K:(\\*FjbmFb`r7$$ \"+8;EA%*FjbmFg`r7%7$$\"+xIP8(*FjbmF]`r7$$\"+,Vdl)*FjbmFb`r7$$\"+mEo!z *FjbmFg`r7%7$$\"+8%z\"35F]\\nF]`r7$$\"+N&*RB5F]\\nFb`r7$$\"+r.\"f,\"F] \\nFg`r7%7$$\"+=:-X5F]\\nF]`r7$$\"+S;Cg5F]\\nFb`r7$$\"+wCv_5F]\\nFg`r7 %7$$\"+BO'=3\"F]\\nF]`r7$$\"+XP3(4\"F]\\nFb`r7$$\"+\"e%f*3\"F]\\nFg`r7 %7$$\"+Gdq=6F]\\nF]`r7$$\"+]e#R8\"F]\\nFb`r7$$\"+'oOk7\"F]\\nFg`r7%7$$ \"+Lyab6F]\\nF]`r7$$\"+bzwq6F]\\nFb`r7$$\"+\"zyK;\"F]\\nFg`r7%7$$\"+Q* *Q#>\"F]\\nF]`r7$$\"+g+h27F]\\nFb`r7$$\"+'*37+7F]\\nFg`r7%7$$\"+(H+%\\ \\Fjbm$\"+F^3W)\\Fjbm$\" +6(\\d%QF]\\n7%7$$\"+]8#yJ&FjbmF[]s7$$\"+c2->aFjbmF`]s7$$\"+Z#HGN&Fjbm Fe]s7%7$$\"+.CC'o&FjbmF[]s7$$\"+4=W(y&FjbmF`]s7$$\"++.D@dFjbmFe]s7%7$$ \"+cMmagFjbmF[]s7$$\"+iG'e:'FjbmF`]s7$$\"+`8n*3'FjbmFe]s7%7$$\"+4X3BkF jbmF[]s7$$\"+:RGClFjbmF`]s7$$\"+1C4ekFjbmFe]s7%7$$\"+ib]\"z'FjbmF[]s7$ $\"+o\\q#*oFjbmF`]s7$$\"+fM^EoFjbmFe]s7%7$$\"+:m#*frFjbmF[]s7$$\"+@g7h sFjbmF`]s7$$\"+7X$\\>(FjbmFe]s7%7$$\"+owMGvFjbmF[]s7$$\"+uqaHwFjbmF`]s 7$$\"+lbNjvFjbmFe]s7%7$$\"+@(on*yFjbmF[]s7$$\"+F\"oz*zFjbmF`]s7$$\"+=m xJzFjbmFe]s7%7$$\"+u(*=l#)FjbmF[]s7$$\"+!=*Qm$)FjbmF`]s7$$\"+rw>+$)Fjb mFe]s7%7$$\"+F3hL')FjbmF[]s7$$\"+L-\"[t)FjbmF`]s7$$\"+C(='o')FjbmFe]s7 %7$$\"+!)=.-!*FjbmF[]s7$$\"+'GJK5*FjbmF`]s7$$\"+x(Rq.*FjbmFe]s7%7$$\"+ LHXq$*FjbmF[]s7$$\"+RBlr%*FjbmF`]s7$$\"+I3Y0%*FjbmFe]s7%7$$\"+')R()Q(* FjbmF[]s7$$\"+#Rt+%)*FjbmF`]s7$$\"+$)=)Qx*FjbmFe]s7%7$$\"+/&H2,\"F]\\n F[]s7$$\"+W%\\3-\"F]\\nF`]s7$$\"+$HIU,\"F]\\nFe]s7%7$$\"+4;dZ5F]\\nF[] s7$$\"+\\:pd5F]\\nF`]s7$$\"+)Rs50\"F]\\nFe]s7%7$$\"+9PT%3\"F]\\nF[]s7$ $\"+aO`%4\"F]\\nF`]s7$$\"+.X\"z3\"F]\\nFe]s7%7$$\"+>eD@6F]\\nF[]s7$$\" +fdPJ6F]\\nF`]s7$$\"+3mvC6F]\\nFe]s7%7$$\"+Cz4e6F]\\nF[]s7$$\"+ky@o6F] \\nF`]s7$$\"+8()fh6F]\\nFe]s7%7$$\"+H+%\\>\"F]\\nF[]s7$$\"+p*f]?\"F]\\ nF`]s7$$\"+=3W)>\"F]\\nFe]s7%7$$\"+$[u`'\\Fjbm$\"+G\"f?&RF]\\n7$$\"+)zFjbmF^js7$$\"+%*)o<#zFjbmFcjs7%7$$\"+gR;\"G)Fjb mFiis7$$\"+%*\\T]$)FjbmF^js7$$\"+Z**=!H)FjbmFcjs7%7$$\"+8]e\\')FjbmFii s7$$\"+Zg$)=()FjbmF^js7$$\"++5he')FjbmFcjs7%7$$\"+mg+=!*FjbmFiis7$$\"+ +rD(3*FjbmF^js7$$\"+`?.F!*FjbmFcjs7%7$$\"+>rU'Q*FjbmFiis7$$\"+`\"ycX*F jbmF^js7$$\"+1JX&R*FjbmFcjs7%7$$\"+s\"[[v*FjbmFiis7$$\"+1#*4C)*FjbmF^j s7$$\"+fT(Qw*FjbmFcjs7%7$$\"+ApK75F]\\nFiis7$$\"+E?D>5F]\\nF^js7$$\"+@ &HK,\"F]\\nFcjs7%7$$\"+F!p\"\\5F]\\nFiis7$$\"+JT4c5F]\\nF^js7$$\"+E;2] 5F]\\nFcjs7%7$$\"+K6,'3\"F]\\nFiis7$$\"+Oi$H4\"F]\\nF^js7$$\"+JP\"p3\" F]\\nFcjs7%7$$\"+PK&G7\"F]\\nFiis7$$\"+T$y(H6F]\\nF^js7$$\"+OevB6F]\\n Fcjs7%7$$\"+U`pf6F]\\nFiis7$$\"+Y/im6F]\\nF^js7$$\"+Tzfg6F]\\nFcjs7%7$ $\"+Zu`'>\"F]\\nFiis7$$\"+^DY.7F]\\nF^js7$$\"+Y+W(>\"F]\\nFcjs7%7$$\"+ I2Yv\\Fjbm$\"+L'HgZ%F]\\n7$$\"+q#RX-&Fjbm$\"+&eaw*\\F]\\n7$$\"+r7Fo\\F jbm$\"+&\\$[$*[F]\\n7%7$$\"+$y\")QM&FjbmFgft7$$\"+B.'HR&FjbmF\\gt7$$\" +CBpO`FjbmFagt7%7$$\"+OGI7dFjbmFgft7$$\"+w8QhdFjbmF\\gt7$$\"+xL60dFjbm Fagt7%7$$\"+*)Qs!3'FjbmFgft7$$\"+HC!)HhFjbmF\\gt7$$\"+IW`tgFjbmFagt7%7 $$\"+U\\9\\kFjbmFgft7$$\"+#[B#)\\'FjbmF\\gt7$$\"+$[b>W'FjbmFagt7%7$$\" +&*fc(zFjbmF\\gt7$$\"+&pRc\"zFjbmFagt7%7$$\"+2-D\"H)FjbmFgft7$$\"+Z(G.M) FjbmF\\gt7$$\"+[21%G)FjbmFagt7%7$$\"+g7nf')FjbmFgft7$$\"++)\\(3()FjbmF \\gt7$$\"+,=[_')FjbmFagt7%7$$\"+8B4G!*FjbmFgft7$$\"+`3fX%*FjbmF\\gt7$$\"+2RK* Q*FjbmFagt7%7$$\"+>W$\\w*FjbmFgft7$$\"+fH,9)*FjbmF\\gt7$$\"+g\\ud(*Fjb mFagt7%7$$\"+ZbL85F]\\nFgft7$$\"+,MC=5F]\\nF\\gt7$$\"+,mh75F]\\nFagt7% 7$$\"+_w<]5F]\\nFgft7$$\"+1b3b5F]\\nF\\gt7$$\"+1(e%\\5F]\\nFagt7%7$$\" +d(>q3\"F]\\nFgft7$$\"+6w#>4\"F]\\nF\\gt7$$\"+63I'3\"F]\\nFagt7%7$$\"+ i='Q7\"F]\\nFgft7$$\"+;(p(G6F]\\nF\\gt7$$\"+;H9B6F]\\nFagt7%7$$\"+nRqg 6F]\\nFgft7$$\"+@=hl6F]\\nF\\gt7$$\"+@])*f6F]\\nFagt7%7$$\"+sga(>\"F] \\nFgft7$$\"+ERX-7F]\\nF\\gt7$$\"+Er#o>\"F]\\nFagt7%7$$\"+Kg.#)\\Fjbm$ \"+&Ha7+&F]\\n7$$\"+oR'z,&Fjbm$\"+.:1DbF]\\n7$$\"+6ANk\\Fjbm$\"+>'p!=a F]\\n7%7$$\"+&3d/N&FjbmFecu7$$\"+@]Q'Q&FjbmFjcu7$$\"+kKxK`FjbmF_du7%7$ $\"+Q\"y)=dFjbmFecu7$$\"+ug![v&FjbmFjcu7$$\"+,dFjbmF_du7%7$$\"+\">* H(3'FjbmFecu7$$\"+FrABhFjbmFjcu7$$\"+q`hpgFjbmF_du7%7$$\"+W-sbkFjbmFec u7$$\"+!=[;\\'FjbmFjcu7$$\"+Bk.QkFjbmF_du7%7$$\"+(HTT#oFjbmFecu7$$\"+L #p+'oFjbmFjcu7$$\"+wuX1oFjbmF_du7%7$$\"+]Bc#>(FjbmFecu7$$\"+'G!\\GsFjb mFjcu7$$\"+H&y[<(FjbmF_du7%7$$\"+.M)4c(FjbmFecu7$$\"+R8\"pf(FjbmFjcu7$ $\"+#e*HVvFjbmF_du7%7$$\"+cWSHzFjbmFecu7$$\"+#RK`'zFjbmFjcu7$$\"+N1s6z FjbmF_du7%7$$\"+4b#yH)FjbmFecu7$$\"+XMvL$)FjbmFjcu7$$\"+)oT,G)FjbmF_du 7%7$$\"+ilCm')FjbmFecu7$$\"+)\\u@q)FjbmFjcu7$$\"+TFc[')FjbmF_du7%7$$\" +:wmM!*FjbmFecu7$$\"+^bfq!*FjbmFjcu7$$\"+%z$)p,*FjbmF_du7%7$$\"+o')3.% *FjbmFecu7$$\"+/m,R%*FjbmFjcu7$$\"+Z[S&Q*FjbmF_du7%7$$\"+@(4:x*FjbmFec u7$$\"+dwV2)*FjbmFjcu7$$\"++f#Qv*FjbmF_du7%7$$\"+xI*R,\"F]\\nFecu7$$\" +ree<5F]\\nFjcu7$$\"+&pCA,\"F]\\nF_du7%7$$\"+#=N30\"F]\\nFecu7$$\"+wzU a5F]\\nFjcu7$$\"++o1\\5F]\\nF_du7%7$$\"+(Gxw3\"F]\\nFecu7$$\"+\"3q74\" F]\\nFjcu7$$\"+0*3f3\"F]\\nF_du7%7$$\"+#R>X7\"F]\\nFecu7$$\"+'=7\"G6F] \\nFjcu7$$\"+55vA6F]\\nF_du7%7$$\"+(\\h8;\"F]\\nFecu7$$\"+\"Ha\\;\"F] \\nFjcu7$$\"+:Jff6F]\\nF_du7%7$$\"+-O?)>\"F]\\nFecu7$$\"+'R'z,7F]\\nFj cu7$$\"+?_V'>\"F]\\nF_du7%7$$\"+o`Z')\\Fjbm$\"+=g-FbF]\\n7$$\"+KY_8]Fj bm$\"+h8#>0'F]\\n7$$\"+_*R<'\\Fjbm$\"+7%3J%fF]\\n7%7$$\"+@k*[N&FjbmFc` v7$$\"+&oX>Q&FjbmFh`v7$$\"+05;I`FjbmF]av7%7$$\"+uuJBdFjbmFc`v7$$\"+QnO ]dFjbmFh`v7$$\"+e?e)p&FjbmF]av7%7$$\"+F&Q<4'FjbmFc`v7$$\"+\"z(y=hFjbmF h`v7$$\"+6J+ngFjbmF]av7%7$$\"+!ef,Y'FjbmFc`v7$$\"+W)3s['FjbmFh`v7$$\"+ kTUNkFjbmF]av7%7$$\"+L1eGoFjbmFc`v7$$\"+(*)Hc&oFjbmFh`v7$$\"+<_%Q!oFjb mF]av7%7$$\"+'o,q>(FjbmFc`v7$$\"+]40CsFjbmFh`v7$$\"+qiEsrFjbmF]av7%7$$ \"+RFUlvFjbmFc`v7$$\"+.?Z#f(FjbmFh`v7$$\"+BtoSvFjbmF]av7%7$$\"+#zVQ$zF jbmFc`v7$$\"+cI*3'zFjbmFh`v7$$\"+w$3\"4zFjbmF]av7%7$$\"+X[E-$)FjbmFc`v 7$$\"+4TJH$)FjbmFh`v7$$\"+H%HvF)FjbmF]av7%7$$\"+)*eoq')FjbmFc`v7$$\"+i ^t(p)FjbmFh`v7$$\"+#[]fk)FjbmF]av7%7$$\"+^p5R!*FjbmFc`v7$$\"+:i:m!*Fjb mFh`v7$$\"+N:P9!*FjbmF]av7%7$$\"+/!GvS*FjbmFc`v7$$\"+osdM%*FjbmFh`v7$$ \"+)e#z#Q*FjbmF]av7%7$$\"+d!\\fx*FjbmFc`v7$$\"+@$)*H!)*FjbmFh`v7$$\"+T O@^(*FjbmF]av7%7$$\"+6qV95F]\\nFc`v7$$\"+P>9<5F]\\nFh`v7$$\"+pM'>,\"F] \\nF]av7%7$$\"+;\"z70\"F]\\nFc`v7$$\"+US)R0\"F]\\nFh`v7$$\"+ub!)[5F]\\ nF]av7%7$$\"+@77)3\"F]\\nFc`v7$$\"+Zh#34\"F]\\nFh`v7$$\"+zwk&3\"F]\\nF ]av7%7$$\"+EL'\\7\"F]\\nFc`v7$$\"+_#ow7\"F]\\nFh`v7$$\"+%y*[A6F]\\nF]a v7%7$$\"+Ja!=;\"F]\\nFc`v7$$\"+d.^k6F]\\nFh`v7$$\"+*)=Lf6F]\\nF]av7%7$ $\"+Ovk)>\"F]\\nFc`v7$$\"+iCN,7F]\\nFh`v7$$\"+%*R<'>\"F]\\nF]av7%7$$\" +^6d*)\\Fjbm$\"+\\O0`gF]\\n7$$\"+\\)G/,&Fjbm$\"+5`_ylF]\\n7$$\"+bU$*f \\Fjbm$\"+Z>[okF]\\n7%7$$\"+/A*zN&FjbmFa]w7$$\"+-*\\)y`FjbmFf]w7$$\"+3 `NG`FjbmF[^w7%7$$\"+dKTEdFjbmFa]w7$$\"+b4FZdFjbmFf]w7$$\"+hjx'p&FjbmF[ ^w7%7$$\"+5V$[4'FjbmFa]w7$$\"+3?p:hFjbmFf]w7$$\"+9u>lgFjbmF[^w7%7$$\"+ j`DjkFjbmFa]w7$$\"+hI6%['FjbmFf]w7$$\"+n%=OV'FjbmF[^w7%7$$\"+;knJoFjbm Fa]w7$$\"+9T`_oFjbmFf]w7$$\"+?&R?!oFjbmF[^w7%7$$\"+pu4+sFjbmFa]w7$$\"+ n^&4A(FjbmFf]w7$$\"+t0YqrFjbmF[^w7%7$$\"+A&=&ovFjbmFa]w7$$\"+?iP*e(Fjb mFf]w7$$\"+E;))QvFjbmF[^w7%7$$\"+v&Rp$zFjbmFa]w7$$\"+tszdzFjbmFf]w7$$ \"+zEI2zFjbmF[^w7%7$$\"+G1O0$)FjbmFa]w7$$\"+E$=iK)FjbmFf]w7$$\"+KPsv#) FjbmF[^w7%7$$\"+\"o\"yt')FjbmFa]w7$$\"+z$RYp)FjbmFf]w7$$\"+&yWTk)FjbmF [^w7%7$$\"+MF?U!*FjbmFa]w7$$\"+K/1j!*FjbmFf]w7$$\"+Qec7!*FjbmF[^w7%7$$ \"+(yB1T*FjbmFa]w7$$\"+&[\"[J%*FjbmFf]w7$$\"+\"*o)4Q*FjbmF[^w7%7$$\"+S [/z(*FjbmFa]w7$$\"+QD!**z*FjbmFf]w7$$\"+WzS\\(*FjbmF[^w7%7$$\"+*eYZ,\" F]\\nFa]w7$$\"+fB$o,\"F]\\nFf]w7$$\"++Hy65F]\\nF[^w7%7$$\"+%p)e^5F]\\n Fa]w7$$\"+kWn`5F]\\nFf]w7$$\"+0]i[5F]\\nF[^w7%7$$\"+*zI%)3\"F]\\nFa]w7 $$\"+pl^!4\"F]\\nFf]w7$$\"+5rY&3\"F]\\nF[^w7%7$$\"+/HFD6F]\\nFa]w7$$\" +u'et7\"F]\\nFf]w7$$\"+:#4B7\"F]\\nF[^w7%7$$\"+4]6i6F]\\nFa]w7$$\"+z2? k6F]\\nFf]w7$$\"+?8:f6F]\\nF[^w7%7$$\"+9r&*)>\"F]\\nFa]w7$$\"+%)G/,7F] \\nFf]w7$$\"+DM*f>\"F]\\nF[^w7%7$$\"+5Cz\"*\\Fjbm$\"+8(3#zlF]\\n7$$\"+ !f2#3]Fjbm$\"+D=+0rF]\\n7$$\"+-nke\\Fjbm$\"+fb4%*pF]\\n7%7$$\"+jM@g`Fj bmF_jw7$$\"+V'GmP&FjbmFdjw7$$\"+bx1F`FjbmFijw7%7$$\"+;XjGdFjbmF_jw7$$ \"+'p\\]u&FjbmFdjw7$$\"+3))[&p&FjbmFijw7%7$$\"+pb0(4'FjbmF_jw7$$\"+\\2 Z8hFjbmFdjw7$$\"+h)4R1'FjbmFijw7%7$$\"+AmZlkFjbmF_jw7$$\"+-=*=['FjbmFd jw7$$\"+94LKkFjbmFijw7%7$$\"+vw*Q$oFjbmF_jw7$$\"+bGJ]oFjbmFdjw7$$\"+n> v+oFjbmFijw7%7$$\"+G(=B?(FjbmF_jw7$$\"+3Rt=sFjbmFdjw7$$\"+?I\"F]\\nF_jw7$$\"+e2#3?\"F]\\nFdjw7$$\"+pY'e>\"F]\\nFijw7 %7$$\"+-iU$*\\Fjbm$\"+&yIa5(F]\\n7$$\"+)ztl+&Fjbm$\"+L8TJwF]\\n7$$\"+i Rqd\\Fjbm$\"+*)4))>vF]\\n7%7$$\"+bs%=O&FjbmF]gx7$$\"+^[*\\P&FjbmFbgx7$ $\"+:]7E`FjbmFggx7%7$$\"+3$o-t&FjbmF]gx7$$\"+/fTVdFjbmFbgx7$$\"+oga%p& FjbmFggx7%7$$\"+h$*o)4'FjbmF]gx7$$\"+dp$=6'FjbmFbgx7$$\"+@r'H1'FjbmFgg x7%7$$\"+9/6nkFjbmF]gx7$$\"+5!e-['FjbmFbgx7$$\"+u\")QJkFjbmFggx7%7$$\" +n9`NoFjbmF]gx7$$\"+j!z'[oFjbmFbgx7$$\"+F#4)*z'FjbmFggx7%7$$\"+?D&R?(F jbmF]gx7$$\"+;,5k)FjbmFggx7%7$$\"+&ydg/*FjbmF]gx7$$\"+\"Q0#f!*FjbmFbgx7$$\"+XbL5!* FjbmFggx7%7$$\"+Q)yWT*FjbmF]gx7$$\"+MkiF%*FjbmFbgx7$$\"+)fc(y$*FjbmFgg x7%7$$\"+\"*)**Gy*FjbmF]gx7$$\"+([Zgz*FjbmFbgx7$$\"+^wu>0\"F]\\nF]gx7$$\"+f*)G`5F]\\nFbgx7$$\"+v>S[5F]\\nFggx7%7$$\"+/j\") )3\"F]\\nF]gx7$$\"+k58!4\"F]\\nFbgx7$$\"+!3W_3\"F]\\nFggx7%7$$\"+4%ec7 \"F]\\nF]gx7$$\"+pJ(p7\"F]\\nFbgx7$$\"+&='3A6F]\\nFggx7%7$$\"+90]i6F] \\nF]gx7$$\"+u_\"Q;\"F]\\nFbgx7$$\"+!HG*e6F]\\nFggx7%7$$\"+>EM*>\"F]\\ nF]gx7$$\"+ztl+7F]\\nFbgx7$$\"+&Rqd>\"F]\\nFggx7%7$$\"+/Tl%*\\Fjbm$\"+ $z*oJwF]\\n7$$\"+'*eM0]Fjbm$\"+1Ryd\")F]\\n7$$\"+?y*p&\\Fjbm$\"+Q/zX!) F]\\n7%7$$\"+d^2j`FjbmF[dy7$$\"+\\pwt`FjbmF`dy7$$\"+t)=aK&FjbmFedy7%7$ $\"+5i\\JdFjbmF[dy7$$\"+-!)=UdFjbmF`dy7$$\"+E*RQp&FjbmFedy7%7$$\"+js\" **4'FjbmF[dy7$$\"+b!416'FjbmF`dy7$$\"+z4EigFjbmFedy7%7$$\"+;$Q$okFjbmF [dy7$$\"+3,.zkFjbmF`dy7$$\"+K?oIkFjbmFedy7%7$$\"+p$fn$oFjbmF[dy7$$\"+h 6XZoFjbmF`dy7$$\"+&3.\"*z'FjbmFedy7%7$$\"+A/=0sFjbmF[dy7$$\"+9A(e@(Fjb mF`dy7$$\"+QT_nrFjbmFedy7%7$$\"+v9gtvFjbmF[dy7$$\"+nKH%e(FjbmF`dy7$$\" +\">Xf`(FjbmFedy7%7$$\"+GD-UzFjbmF[dy7$$\"+?Vr_zFjbmF`dy7$$\"+WiO/zFjb mFedy7%7$$\"+\"eV/J)FjbmF[dy7$$\"+t`8@$)FjbmF`dy7$$\"+(H(ys#)FjbmFedy7 %7$$\"+MY')y')FjbmF[dy7$$\"+Ekb*o)FjbmF`dy7$$\"+]$37k)FjbmFedy7%7$$\"+ (o&GZ!*FjbmF[dy7$$\"+zu(z0*FjbmF`dy7$$\"+.%H'4!*FjbmFedy7%7$$\"+Snq:%* FjbmF[dy7$$\"+K&)RE%*FjbmF`dy7$$\"+c/0y$*FjbmFedy7%7$$\"+$zFTy*FjbmF[d y7$$\"+&e>[z*FjbmF`dy7$$\"+4:ZY(*FjbmFedy7%7$$\"+%)[D:5F]\\nF[dy7$$\"+ kSK;5F]\\nF`dy7$$\"+c#*[65F]\\nFedy7%7$$\"+*)p4_5F]\\nF[dy7$$\"+ph;`5F ]\\nF`dy7$$\"+h8L[5F]\\nFedy7%7$$\"+%4R*)3\"F]\\nF[dy7$$\"+u#3+4\"F]\\ nF`dy7$$\"+mM<&3\"F]\\nFedy7%7$$\"+*>\"yD6F]\\nF[dy7$$\"+z.&o7\"F]\\nF `dy7$$\"+rb,A6F]\\nFedy7%7$$\"+/Lii6F]\\nF[dy7$$\"+%[#pj6F]\\nF`dy7$$ \"+ww&)e6F]\\nFedy7%7$$\"+4aY*>\"F]\\nF[dy7$$\"+*eM0?\"F]\\nF`dy7$$\"+ \"y*p&>\"F]\\nFedy7%7$$\"+AXf&*\\Fjbm$\"+6+(z:)F]\\n7$$\"+yaS/]Fjbm$\" +n_8%o)F]\\n7$$\"+!Rek&\\Fjbm$\"+L0zr&)F]\\n7%7$$\"+vb,k`FjbmFi`z7$$\" +Jl#GP&FjbmF^az7$$\"+V%z[K&FjbmFcaz7%7$$\"+GmVKdFjbmFi`z7$$\"+%eZ7u&Fj bmF^az7$$\"+'\\+Lp&FjbmFcaz7%7$$\"+\"od35'FjbmFi`z7$$\"+P'o'4hFjbmF^az 7$$\"+\\:shgFjbmFcaz7%7$$\"+M(y#pkFjbmFi`z7$$\"+!p*3ykFjbmF^az7$$\"+-E 9IkFjbmFcaz7%7$$\"+(y*pPoFjbmFi`z7$$\"+V2^YoFjbmF^az7$$\"+bOc)z'FjbmFc az7%7$$\"+S371sFjbmFi`z7$$\"+'zJ\\@(FjbmF^az7$$\"+3Z)p;(FjbmFcaz7%7$$ \"+$*=auvFjbmFi`z7$$\"+\\GN$e(FjbmF^az7$$\"+hdSNvFjbmFcaz7%7$$\"+YH'H% zFjbmFi`z7$$\"+-Rx^zFjbmF^az7$$\"+9o#Q!zFjbmFcaz7%7$$\"+**RQ6$)FjbmFi` z7$$\"+b\\>?$)FjbmF^az7$$\"+nyCs#)FjbmFcaz7%7$$\"+_]!)z')FjbmFi`z7$$\" +3gh)o)FjbmF^az7$$\"+?*o1k)FjbmFcaz7%7$$\"+0hA[!*FjbmFi`z7$$\"+hq.d!*F jbmF^az7$$\"+t**34!*FjbmFcaz7%7$$\"+erk;%*FjbmFi`z7$$\"+9\"eaU*FjbmF^a z7$$\"+E5^x$*FjbmFcaz7%7$$\"+6#o]y*FjbmFi`z7$$\"+n\"zQz*FjbmF^az7$$\"+ z?$fu*FjbmFcaz7%7$$\"+E*[`,\"F]\\nFi`z7$$\"+A+B;5F]\\nF^az7$$\"+8`V65F ]\\nFcaz7%7$$\"+J5>_5F]\\nFi`z7$$\"+F@2`5F]\\nF^az7$$\"+=uF[5F]\\nFcaz 7%7$$\"+OJ.*3\"F]\\nFi`z7$$\"+KU\"**3\"F]\\nF^az7$$\"+B&>^3\"F]\\nFcaz 7%7$$\"+T_(e7\"F]\\nFi`z7$$\"+PjvE6F]\\nF^az7$$\"+G;'>7\"F]\\nFcaz7%7$ $\"+Ytri6F]\\nFi`z7$$\"+U%)fj6F]\\nF^az7$$\"+LP!)e6F]\\nFcaz7%7$$\"+^% f&*>\"F]\\nFi`z7$$\"+Z0W+7F]\\nF^az7$$\"+Qek&>\"F]\\nFcaz7%7$$\"+/oK'* \\Fjbm$\"+dGE%o)F]\\n7$$\"+'>tO+&Fjbm$\"+,SZ5#*F]\\n7$$\"+!=Rg&\\Fjbm$ \"+-y&y4*F]\\n7%7$$\"+dyuk`FjbmFg][l7$$\"+\\U4s`FjbmF\\^[l7$$\"+L-YC`F jbmFa^[l7%7$$\"+5*oJt&FjbmFg][l7$$\"+-`^SdFjbmF\\^[l7$$\"+'G\")Gp&Fjbm Fa^[l7%7$$\"+j**e,hFjbmFg][l7$$\"+bj$*3hFjbmF\\^[l7$$\"+RBIhgFjbmFa^[l 7%7$$\"+;5,qkFjbmFg][l7$$\"+3uNxkFjbmF\\^[l7$$\"+#RB(HkFjbmFa^[l7%7$$ \"+p?VQoFjbmFg][l7$$\"+h%yd%oFjbmF\\^[l7$$\"+XW9)z'FjbmFa^[l7%7$$\"+AJ &o?(FjbmFg][l7$$\"+9&*>9sFjbmF\\^[l7$$\"+)\\ll;(FjbmFa^[l7%7$$\"+vTFvv FjbmFg][l7$$\"+n0i#e(FjbmF\\^[l7$$\"+^l)\\`(FjbmFa^[l7%7$$\"+G_pVzFjbm Fg][l7$$\"+?;/^zFjbmF\\^[l7$$\"+/wS.zFjbmFa^[l7%7$$\"+\"G;@J)FjbmFg][l 7$$\"+tEY>$)FjbmF\\^[l7$$\"+d'G=F)FjbmFa^[l7%7$$\"+Mt`!o)FjbmFg][l7$$ \"+EP)yo)FjbmF\\^[l7$$\"+5(\\-k)FjbmFa^[l7%7$$\"+(Qe*[!*FjbmFg][l7$$\" +zZIc!*FjbmF\\^[l7$$\"+j2n3!*FjbmFa^[l7%7$$\"+S%ztT*FjbmFg][l7$$\"+Kes C%*FjbmF\\^[l7$$\"+;=4x$*FjbmFa^[l7%7$$\"+$\\+ey*FjbmFg][l7$$\"+&)o9$z *FjbmF\\^[l7$$\"+pG^X(*FjbmFa^[l7%7$$\"+a@U:5F]\\nFg][l7$$\"+%zch,\"F] \\nF\\^[l7$$\"+#R$R65F]\\nFa^[l7%7$$\"+fUE_5F]\\nFg][l7$$\"+**))*H0\"F ]\\nF\\^[l7$$\"+(\\N#[5F]\\nFa^[l7%7$$\"+kj5*3\"F]\\nFg][l7$$\"+/5%)*3 \"F]\\nF\\^[l7$$\"+-w2&3\"F]\\nFa^[l7%7$$\"+p%[f7\"F]\\nFg][l7$$\"+4Jo E6F]\\nF\\^[l7$$\"+2(>>7\"F]\\nFa^[l7%7$$\"+u0zi6F]\\nFg][l7$$\"+9__j6 F]\\nF\\^[l7$$\"+7=we6F]\\nFa^[l7%7$$\"+zEj*>\"F]\\nFg][l7$$\"+>tO+7F] \\nF\\^[l7$$\"+\"F]\\nFa^[l7%7$$\"+Wa!p*\\Fjbm$\"+fMc5#*F]\\n7$$ \"+cX4.]Fjbm$\"+z\\!ot*F]\\n7$$\"+T%3d&\\Fjbm$\"+Zb(Ri*F]\\n7%7$$\"+( \\E`O&FjbmFej[l7$$\"+4c^r`FjbmFjj[l7$$\"+%\\HTK&FjbmF_[\\l7%7$$\"+]vuL dFjbmFej[l7$$\"+im$*RdFjbmFjj[l7$$\"+Z0b#p&FjbmF_[\\l7%7$$\"+.'o@5'Fjb mFej[l7$$\"+:xN3hFjbmFjj[l7$$\"++;(41'FjbmF_[\\l7%7$$\"+c'*eqkFjbmFej[ l7$$\"+o(ynZ'FjbmFjj[l7$$\"+`ERHkFjbmF_[\\l7%7$$\"+42,RoFjbmFej[l7$$\" +@)*>XoFjbmFjj[l7$$\"+1P\"yz'FjbmF_[\\l7%7$$\"+i/#e(Fjb mFjj[l7$$\"+7elMvFjbmF_[\\l7%7$$\"+oQFWzFjbmFej[l7$$\"+!)HY]zFjbmFjj[l 7$$\"+lo2.zFjbmF_[\\l7%7$$\"+@\\p7$)FjbmFej[l7$$\"+LS))=$)FjbmFjj[l7$$ \"+=z\\r#)FjbmF_[\\l7%7$$\"+uf6\"o)FjbmFej[l7$$\"+'30to)FjbmFjj[l7$$\" +r*=*R')FjbmF_[\\l7%7$$\"+Fq`\\!*FjbmFej[l7$$\"+Rhsb!*FjbmFjj[l7$$\"+C +M3!*FjbmF_[\\l7%7$$\"+!3ezT*FjbmFej[l7$$\"+#>ZTU*FjbmFjj[l7$$\"+x5ww$ *FjbmF_[\\l7%7$$\"+L\"zjy*FjbmFej[l7$$\"+X#oDz*FjbmFjj[l7$$\"+I@=X(*Fj bmF_[\\l7%7$$\"+=+[:5F]\\nFej[l7$$\"+I*)4;5F]\\nFjj[l7$$\"+=.O65F]\\nF _[\\l7%7$$\"+B@K_5F]\\nFej[l7$$\"+N5%H0\"F]\\nFjj[l7$$\"+BC?[5F]\\nF_[ \\l7%7$$\"+GU;*3\"F]\\nFej[l7$$\"+SJy*3\"F]\\nFjj[l7$$\"+GX/&3\"F]\\nF _[\\l7%7$$\"+Lj+E6F]\\nFej[l7$$\"+X_iE6F]\\nFjj[l7$$\"+Lm)=7\"F]\\nF_[ \\l7%7$$\"+Q%[G;\"F]\\nFej[l7$$\"+]tYj6F]\\nFjj[l7$$\"+Q(G(e6F]\\nF_[ \\l7%7$$\"+V0p*>\"F]\\nFej[l7$$\"+b%4.?\"F]\\nFjj[l7$$\"+V3d&>\"F]\\nF _[\\l7%7$$\"+!pot*\\Fjbm$\"+k*oot*F]\\n7$$\"+58j-]Fjbm$\"+1JJE5F_bm7$$ \"+')RWb\\Fjbm$\"+tJ,:5F_bm7%7$$\"+V(*yl`FjbmFcg\\l7$$\"+jB0r`FjbmFhg \\l7$$\"+R]'QK&FjbmF]h\\l7%7$$\"+'z5Ut&FjbmFcg\\l7$$\"+;MZRdFjbmFhg\\l 7$$\"+#4'G#p&FjbmF]h\\l7%7$$\"+\\=j-hFjbmFcg\\l7$$\"+pW*y5'FjbmFhg\\l7 $$\"+XrqggFjbmF]h\\l7%7$$\"+-H0rkFjbmFcg\\l7$$\"+AbJwkFjbmFhg\\l7$$\"+ )>G\"HkFjbmF]h\\l7%7$$\"+bRZRoFjbmFcg\\l7$$\"+vltWoFjbmFhg\\l7$$\"+^# \\vz'FjbmF]h\\l7%7$$\"+3]*y?(FjbmFcg\\l7$$\"+Gw:8sFjbmFhg\\l7$$\"+/.(f ;(FjbmF]h\\l7%7$$\"+hgJwvFjbmFcg\\l7$$\"+\"oy:e(FjbmFhg\\l7$$\"+d8RMvF jbmF]h\\l7%7$$\"+9rtWzFjbmFcg\\l7$$\"+M(***\\zFjbmFhg\\l7$$\"+5C\"G!zF jbmF]h\\l7%7$$\"+n\"eJJ)FjbmFcg\\l7$$\"+(y?%=$)FjbmFhg\\l7$$\"+jMBr#)F jbmF]h\\l7%7$$\"+?#z:o)FjbmFcg\\l7$$\"+S=%oo)FjbmFhg\\l7$$\"+;XlR')Fjb mF]h\\l7%7$$\"+t-+]!*FjbmFcg\\l7$$\"+$*GEb!*FjbmFhg\\l7$$\"+pb23!*Fjbm F]h\\l7%7$$\"+E8U=%*FjbmFcg\\l7$$\"+YRoB%*FjbmFhg\\l7$$\"+Am\\w$*FjbmF ]h\\l7%7$$\"+zB%oy*FjbmFcg\\l7$$\"+**\\5#z*FjbmFhg\\l7$$\"+vw\"\\u*Fjb mF]h\\l7%7$$\"+Vj_:5F]\\nFcg\\l7$$\"+0E0;5F]\\nFhg\\l7$$\"+tQL65F]\\nF ]h\\l7%7$$\"+[%oB0\"F]\\nFcg\\l7$$\"+5Z*G0\"F]\\nFhg\\l7$$\"+yf<[5F]\\ nF]h\\l7%7$$\"+`0@*3\"F]\\nFcg\\l7$$\"+:ot*3\"F]\\nFhg\\l7$$\"+$3=]3\" F]\\nF]h\\l7%7$$\"+eE0E6F]\\nFcg\\l7$$\"+?*yl7\"F]\\nFhg\\l7$$\"+)=g=7 \"F]\\nF]h\\l7%7$$\"+jZ*G;\"F]\\nFcg\\l7$$\"+D5Uj6F]\\nFhg\\l7$$\"+$H- (e6F]\\nF]h\\l7%7$$\"+oot*>\"F]\\nFcg\\l7$$\"+IJE+7F]\\nFhg\\l7$$\"+)R Wb>\"F]\\nF]h\\l-Fjam6&F\\bm$\")=THvF_bmF_d]lF_d]l-%+AXESLABELSG6$%\"x G%\"yG-%%VIEWG6$;$\"++++]YFjbm$\"++++N7F]\\n;$!+++++]Fjbm$\"++++]5F_bm " 2 492 363 363 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 508 35 "Third example: (A lin ear equation)\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "diff_eq : = diff(y(x),x) - 2*y(x) = -3*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% (diff_eqG/,&-%%diffG6$-%\"yG6#%\"xGF-\"\"\"F*!\"#,$F-!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Bernoulli_ode(diff_eq);" }}{PARA 6 "" 1 "" {TEXT -1 45 "Equation is linear. Switching to type linear:" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7)/,&-%%diffG6$-%\"yG6#%\"xGF,\"\"\"F) !\"#,$F,!\"$/*&-%$expG6#-%$IntG6$F.F,F-F%F-,$*&F3F-F,F-F0/-%%DiffG6$** %\"(GF-F3F-F)F-%\")GF-F,F9/*&F3F-F)F-,&-F76$F9F,F-%#_CGF-/*&-F46#,$F,F .F-F)F-,&-F76$,$*&FJF-F,F-F0F,F-FGF-/FI,(FQ#\"\"$\"\"#FJ#FU\"\"%FGF-/F )*&-F46#,$F,FVF-FSF-" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 506 38 "Fourth example: (A separ able equation)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "diff_eq := diff(y(x),x) - 2*y(x) = -3*x*y(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(diff_eqG/,&-%%diffG6$-%\"yG6#%\"x GF-\"\"\"F*!\"#,$*&F-F.F*F.!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Bernoulli_ode(diff_eq);" }}{PARA 6 "" 1 "" {TEXT -1 51 "Equati on is separable. Switching to type separable:" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7&/,&-%%diffG6$-%\"yG6#%\"xGF,\"\"\"F)!\"#,$*&F,F-F)F-! \"$/F&*&,&F,F1\"\"#F-F-F)F-/-%$IntG6$*$F*!\"\"F*,&-F86$F4F,F-%#_CGF-/- %#lnG6#F),(*$F,F5#F1F5F,F5F?F-" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 441 14 "Fifth Example:" }{TEXT -1 2 "\n\n" } {TEXT 484 66 "A differential equation of Bernoulli type with initial c ondition.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "ode := diff(y (x),x) + y(x) = 1/y(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG/,& -%%diffG6$-%\"yG6#%\"xGF-\"\"\"F*F.*$F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ic := y(3) = 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#icG/-%\"yG6#\"\"$\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Bernoulli_ode(ode,ic);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7-/,&-%%diffG6$-%\"yG6#%\"xGF,\"\"\"F) F-*$F)!\"\"/-%%zetaGF+*$F)\"\"#/,&-F'6$F1F,F-F1F4F4/*&-%$expG6#-%$IntG 6$F4F,F-F6F-,$F;F4/-%%DiffG6$**%\"(GF-F;F-F1F-%\")GF-F,FA/*&F;F-F1F-,& -F?6$FAF,F-%\"CGF-/*&-F<6#,$F,F4F-F1F-,&-F?6$,$FQF4F,F-FNF-/FP,&FQF-FN F-/F1*&-F<6#,$F,!\"#F-FYF-/F1*&-F<6#,&F,Fin\"\"'F-F-,&*&F,F--F<6#,&F,F 4!\"'F-F-F4FboFinF-/F3F[o" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "Again let's plot a solution curve:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "dfplot \+ := dfieldplot(ode, y(x), x = 1 .. 5, y = 1 ..3, color = gray):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "soln_plot := implicitplot(y ^2 = exp(-2*x+6)*(2*x*exp(2*x-6)-2*exp(2*x-6)), x = 1 .. 5, y = 1 ..3, color = magenta, thickness=2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display(\{dfplot, soln_plot\});" }}{PARA 13 "" 1 "" {INLPLOT " 6&-%'CURVESG6fp7$7$$\"1+++++++:!#:$\"\"\"\"\"!7$$\"10@%ot%*ya\"F*$\"1Z *y:j_g/\"F*7$7$$\"1+++++?$e\"F*$\"1++++++!3\"F*F.7$F47$$\"1W(*eV(*e.;F *$\"1G^?G^?)4\"F*7$7$$\"1++++++S;F*$\"1&G9dG928\"F*F:7$F@7$$\"1Tc-Tc-h ;F*$\"1zr[zr[\\6F*7$7$$\"1+++++!Gn\"F*$\"1++++++g6F*FF7$FL7$$\"1+++++] ?\"F*7$7$$\"1,++++!)o7&>7&\\7F*7$7$$\"1+++++++=F*$\"1********\\Pk7F*Fhn7$F^o7 $$\"1Uj9MYTV=F*$\"1Ho#Ho#H)H\"F*7$7$$\"1,++++?r=F*$\"1++++++?8F*Fdo7$F jo7$$\"1eG9dG92>F*$\"1r&G9dGkM\"F*7$7$$\"1++++++g>F*$\"1eqkw/>(>F*$\"1>w/>w/%R\"F*7$7$$\"1,+++++!)>F*$\"1+++++++9 F*F\\q7$Fbq7$$\"1\"zi6l/'Q?F*$\"1/'=Wn(pS9F*7$7$$\"1,++++?&4#F*$\"1+++ +++![\"F*Fhq7$F^r7$$\"1\"44444f5#F*$\"1aaaaa/([\"F*7$7$$\"1++++++?@F*$ \"1%ot%*y:j\\\"F*Fdr7$Fjr7$$\"1,+++++v@F*$\"1+++++]K:F*7$7$$\"1,++++!o @#F*$\"1++++++g:F*F`s7$Ffs7$$\"1*))))))))))[C#F*$\"1bbbbbbx:F*7$7$$\"1 ++++++!G#F*$\"1+++++]*f\"F*F\\t7$Fbt7$$\"1,+++++;BF*$\"1,+++++A;F*7$7$ $\"1,++++![M#F*$\"1,+++++S;F*Fht7$F^u7$$\"1=_cp3E)Q#F*$\"1#R<_cpem\"F* 7$7$$\"1++++++SCF*$\"1nmmmmm'p\"F*Fdu7$Fju7$$\"1)3EyM/8Y#F*$\"1dp3EyM4 F*7$7$$\"1************>HF*$\"1MLLLLef>F*F_ z7$7$$\"1++++++?HF*Fhz7$$\"12`Ej\"3/#HF*$\"1[tO=fzf>F*7$7$$\"1,++++!3# HF*$\"1,+++++g>F*F^[l7$Fd[l7$$\"1,++++S+IF*$\"1,++++!)**>F*7$7$$\"1,++ +++!3$F*$\"1,++++gR?F*Fj[l7$F`\\l7$$\"1,++++S!3$F*$\"1,++++!)R?F*7$7$$ \"1-++++!33$F*$\"1,+++++S?F*Ff\\l7$F\\]l7$$\"1FPJ%yg>;$F*$\"1QJ%yg>!z? F*7$7$$\"1,+++++SKF*$\"1i%Q:YQl6#F*Fb]l7$Fh]l7$$\"13Zw6%HNC$F*$\"1Zw6% HN#=@F*7$7$$\"1-++++?ZKF*$\"1,+++++?@F*F^^l7$7$$\"1.++++?ZKF*Fg^l7$$\" 1j%Q:YQlK$F*$\"1q2Bp2tc@F*7$7$$\"1,++++++MF*$\"1U2uS2u!>#F*F]_l7$Fc_l7 $$\"1'Q:YQ:'4MF*$\"14Bp2B>&>#F*7$7$$\"1-+++++?MF*$\"1,++++++AF*Fi_l7$F _`l7$$\"1X4:kA'R\\$F*$\"1HX#z')=IB#F*7$7$$\"1,+++++gNF*$\"1,++++]iAF*F e`l7$F[al7$$\"1Qx.m0\\yNF*$\"1L6)pra2F#F*7$7$$\"1-++++?*f$F*$\"1,+++++ !G#F*Faal7$Fgal7$$\"1wS2uS2kOF*$\"1jH'H'H'zI#F*7$7$$\"1-+++++?PF*$\"1U s^l*o?L#F*F]bl7$7$$\"1,+++++?PF*Ffbl7$$\"1-+++++]PF*$\"1,+++++XBF*7$7$ $\"1.++++![y$F*$\"1,+++++gBF*F\\cl7$Fbcl7$$\"1usssssOQF*$\"1kjjjjj\"Q# F*7$7$$\"1,+++++!)QF*$\"1nmmmmm*R#F*Fhcl7$F^dl7$$\"1-+++++CRF*$\"1,+++ ++=CF*7$7$$\"1.++++!o(RF*F[vFddl7$7$F[el$\"1,+++++SCF*7$$\"1;dG9dy6SF* $\"1Vr&G92TX#F*7$7$$\"1,+++++SSF*$\"1Ux'4(Q[lCF*Fael7$Fgel7$$\"1Xr&G9d .5%F*$\"1H9dG9#)*[#F*7$7$$\"1.++++?vTF*$\"1,+++++?DF*F]fl7$Fcfl7$$\"1X v,2G7*=%F*$\"1H7\\'fQa_#F*7$7$$\"1,++++++UF*$\"1++++voHDF*Fifl7$F_gl7$ $\"1b5Uot%*yUF*$\"1u%*y:j_gDF*7$7$$\"1,+++++gVF*$\"1++++v=#f#F*Fegl7$F [hl7$$\"1lX#)H>xoVF*$\"1?x3NSh&f#F*7$7$$\"1/+++++!Q%F*$\"1,++++++EF*Fa hl7$Fghl7$$\"1'z8C\"=%H Fi^mFg^m7$$\"+y-*y*GFi^mF]_m7%7$$\"+X!)=eIFi^mFc^m7$$\"+v#QB:$Fi^mFg^m 7$$\"+%f;%3JFi^mF]_m7%7$$\"+hVroKFi^mFc^m7$$\"+\"fkGO$Fi^mFg^m7$$\"+5H %*=LFi^mF]_m7%7$$\"+x1CzMFi^mFc^m7$$\"+24RtNFi^mFg^m7$$\"+E#p%HNFi^mF] _m7%7$$\"+$*pw*o$Fi^mFc^m7$$\"+Bs\"Ry$Fi^mFg^m7$$\"+Ub**RPFi^mF]_m7%7$ $\"+4LH+RFi^mFc^m7$$\"+RNW%*RFi^mFg^m7$$\"+e=_]RFi^mF]_m7%7$$\"+D'>36% Fi^mFc^m7$$\"+b)p\\?%Fi^mFg^m7$$\"+u\"[5;%Fi^mF]_m7%7$$\"+TfM@VFi^mFc^ m7$$\"+rh\\:WFi^mFg^m7$$\"+!\\u:P%Fi^mF]_m7%7$$\"+dA(=`%Fi^mFc^m7$$\"+ ([Agi%Fi^mFg^m7$$\"+135#e%Fi^mF]_m7%7$$\"+t&)RUZFi^mFc^m7$$\"+.)[l$[Fi ^mFg^m7$$\"+Ari#z%Fi^mF]_m7%7$$\"+*)[#H&\\Fi^mFc^m7$$\"+>^2Z]Fi^mFg^m7 $$\"+QM:.]Fi^mF]_m7%7$$\"+Cn&3\\*Fe^m$\"+9y>f5Fi^m7$$\"+GV\"40\"Fi^m$ \"+-&G8:\"Fi^m7$$\"+0^$e+\"Fi^m$\"+9fuP6Fi^m7%7$$\"+))>hf6Fi^mFa[n7$$ \"+W1Wh7Fi^mFf[n7$$\"+@9O;7Fi^mF[\\n7%7$$\"+/$Q,P\"Fi^mFa[n7$$\"+gp'>Z \"Fi^mFf[n7$$\"+Px)oU\"Fi^mF[\\n7%7$$\"+?Ym!e\"Fi^mFa[n7$$\"+wK\\#o\"F i^mFf[n7$$\"+`STP;Fi^mF[\\n7%7$$\"+O4>\"z\"Fi^mFa[n7$$\"+#f>I*=Fi^mFf[ n7$$\"+p.%z%=Fi^mF[\\n7%7$$\"+_sr,?Fi^mFa[n7$$\"+3fa.@Fi^mFf[n7$$\"+&o m%e?Fi^mF[\\n7%7$$\"+oNC7AFi^mFa[n7$$\"+CA29BFi^mFf[n7$$\"+,I**oAFi^mF [\\n7%7$$\"+%))pFU#Fi^mFa[n7$$\"+S&)fCDFi^mFf[n7$$\"+<$>&zCFi^mF[\\n7% 7$$\"++iHLEFi^mFa[n7$$\"+c[7NFFi^mFf[n7$$\"+Lc/!p#Fi^mF[\\n7%7$$\"+;D# Q%GFi^mFa[n7$$\"+s6lXHFi^mFf[n7$$\"+\\>d+HFi^mF[\\n7%7$$\"+K)[V0$Fi^mF a[n7$$\"+)[xh:$Fi^mFf[n7$$\"+l#)46JFi^mF[\\n7%7$$\"+[^([E$Fi^mFa[n7$$ \"+/QqmLFi^mFf[n7$$\"+\"eC;K$Fi^mF[\\n7%7$$\"+k9SvMFi^mFa[n7$$\"+?,BxN Fi^mFf[n7$$\"+(*3:KNFi^mF[\\n7%7$$\"+!yFfo$Fi^mFa[n7$$\"+Okv(y$Fi^mFf[ n7$$\"+8snUPFi^mF[\\n7%7$$\"+'4ak*QFi^mFa[n7$$\"+_FG)*RFi^mFf[n7$$\"+H N?`RFi^mF[\\n7%7$$\"+7/)p5%Fi^mFa[n7$$\"+o!4)3UFi^mFf[n7$$\"+X)HP;%Fi^ mF[\\n7%7$$\"+Gn]WFi^mFf[n7$$\"+hhDuVFi^mF[\\n7%7 $$\"+WI.GXFi^mFa[n7$$\"++<')HYFi^mFf[n7$$\"+xCy%e%Fi^mF[\\n7%7$$\"+g$f &QZFi^mFa[n7$$\"+;!)QS[Fi^mFf[n7$$\"+$z3`z%Fi^mF[\\n7%7$$\"+wc3\\\\Fi^ mFa[n7$$\"+KV\"40&Fi^mFf[n7$$\"+4^$e+&Fi^mF[\\n7%7$$\"+[X%\\X*Fe^m$\"+ '***\\l6Fi^m7$$\"+Xb]a5Fi^m$\"+OEbb7Fi^m7$$\"+#z!R35Fi^m$\"+h)oGC\"Fi^ m7%7$$\"+r2-c6Fi^mF_hn7$$\"+h=.l7Fi^mFdhn7$$\"+3r\"*=7Fi^mFihn7%7$$\"+ (3ZlO\"Fi^mF_hn7$$\"+x\"ebZ\"Fi^mFdhn7$$\"+CMWH9Fi^mFihn7%7$$\"+.M2x:F i^mF_hn7$$\"+$\\%3'o\"Fi^mFdhn7$$\"+S(p*R;Fi^mFihn7%7$$\"+>(*f(y\"Fi^m F_hn7$$\"+43h'*=Fi^mFdhn7$$\"+cg\\]=Fi^mFihn7%7$$\"+Ng7)*>Fi^mF_hn7$$ \"+Dr82@Fi^mFdhn7$$\"+sB-h?Fi^mFihn7%7$$\"+^Bl3AFi^mF_hn7$$\"+TMmCFi^mF_hn7$$\"+d(*=GDFi^mFdhn7$ $\"+/]2#[#Fi^mFihn7%7$$\"+$)\\qHEFi^mF_hn7$$\"+tgrQFFi^mFdhn7$$\"+?8g# p#Fi^mFihn7%7$$\"+*HJ-%GFi^mF_hn7$$\"+*QU#\\HFi^mFdhn7$$\"+Ow7.HFi^mFi hn7%7$$\"+:wv]IFi^mF_hn7$$\"+0(o(fJFi^mFdhn7$$\"+_Rl8JFi^mFihn7%7$$\"+ JRGhKFi^mF_hn7$$\"+@]HqLFi^mFdhn7$$\"+o-=CLFi^mFihn7%7$$\"+Z-\"=Z$Fi^m F_hn7$$\"+P8#3e$Fi^mFdhn7$$\"+%e1Z`$Fi^mFihn7%7$$\"+jlL#o$Fi^mF_hn7$$ \"+`wM\"z$Fi^mFdhn7$$\"++HBXPFi^mFihn7%7$$\"+zG'G*QFi^mF_hn7$$\"+pR(=+ %Fi^mFdhn7$$\"+;#fd&RFi^mFihn7%7$$\"+&>*Q.TFi^mF_hn7$$\"+&G+C@%Fi^mFdh n7$$\"+KbGmTFi^mFihn7%7$$\"+6b\"RJ%Fi^mF_hn7$$\"+,m#HU%Fi^mFdhn7$$\"+[ =\"oP%Fi^mFihn7%7$$\"+F=WCXFi^mF_hn7$$\"+n_6Fi^mF]eo7$$\"+&o!Qo7Fi^mFbeo7$$\"+[VM@7 Fi^mFgeo7%7$$\"+j#)>j8Fi^mF]eo7$$\"+,q!*y9Fi^mFbeo7$$\"+k1(=V\"Fi^mFge o7%7$$\"+zXst:Fi^mF]eo7$$\"+Fi^mF]eo7$$\"+\\f[5@Fi^mFbeo7$$\"+7'\\M1#Fi^mFgeo7%7$$\"+FNI0AFi^mF] eo7$$\"+lA,@BFi^mFbeo7$$\"+Gf(RF#Fi^mFgeo7%7$$\"+V)HeT#Fi^mF]eo7$$\"+ \"eQ:`#Fi^mFbeo7$$\"+WA]%[#Fi^mFgeo7%7$$\"+fhNEEFi^mF]eo7$$\"+(*[1UFFi ^mFbeo7$$\"+g&G]p#Fi^mFgeo7%7$$\"+vC)o$GFi^mF]eo7$$\"+87f_HFi^mFbeo7$$ \"+w[b0HFi^mFgeo7%7$$\"+\"z3u/$Fi^mF]eo7$$\"+Hv6jJFi^mFbeo7$$\"+#>\"3; JFi^mFgeo7%7$$\"+2^$zD$Fi^mF]eo7$$\"+XQktLFi^mFbeo7$$\"+3vgELFi^mFgeo7 %7$$\"+B9YoMFi^mF]eo7$$\"+h,<%e$Fi^mFbeo7$$\"+CQ8PNFi^mFgeo7%7$$\"+Rx) *yOFi^mF]eo7$$\"+xkp%z$Fi^mFbeo7$$\"+S,mZPFi^mFgeo7%7$$\"+bS^*)QFi^mF] eo7$$\"+$zA_+%Fi^mFbeo7$$\"+ck=eRFi^mFgeo7%7$$\"+r./+TFi^mF]eo7$$\"+4 \"\\d@%Fi^mFbeo7$$\"+sFroTFi^mFgeo7%7$$\"+(om0J%Fi^mF]eo7$$\"+DaFEWFi^ mFbeo7$$\"+)3R#zVFi^mFgeo7%7$$\"+.I4@XFi^mF]eo7$$\"+T$>;t%Fi^mF]eo7$$\"+d!Gt%[Fi^mFbeo7$$\"+?Fi^mF`bp7$$\"+%*=Ab=Fi^mFebp7 %7$$\"+3Cm\"*>Fi^mF[bp7$$\"+_2g8@Fi^mF`bp7$$\"+5#[d1#Fi^mFebp7%7$$\"+C ()=-AFi^mF[bp7$$\"+oq7CBFi^mF`bp7$$\"+EXFwAFi^mFebp7%7$$\"+S]r7CFi^mF[ bp7$$\"+%Q`Y`#Fi^mF`bp7$$\"+U3!o[#Fi^mFebp7%7$$\"+c8CBEFi^mF[bp7$$\"++ (z^u#Fi^mF`bp7$$\"+erK(p#Fi^mFebp7%7$$\"+swwLGFi^mF[bp7$$\"+;gqbHFi^mF `bp7$$\"+uM&y!HFi^mFebp7%7$$\"+))RHWIFi^mF[bp7$$\"+KBBmJFi^mF`bp7$$\"+ !zz$=JFi^mFebp7%7$$\"+/.#[D$Fi^mF[bp7$$\"+['enP$Fi^mF`bp7$$\"+1h!*GLFi ^mFebp7%7$$\"+?mMlMFi^mF[bp7$$\"+k\\G(e$Fi^mF`bp7$$\"+ACVRNFi^mFebp7%7 $$\"+OH(en$Fi^mF[bp7$$\"+!G6yz$Fi^mF`bp7$$\"+Q(e*\\PFi^mFebp7%7$$\"+_# *R')QFi^mF[bp7$$\"+'fP$3SFi^mF`bp7$$\"+a][gRFi^mFebp7%7$$\"+ob#p4%Fi^m F[bp7$$\"+7R')=UFi^mF`bp7$$\"+q8,rTFi^mFebp7%7$$\"+%)=X2VFi^mF[bp7$$\" +G-RHWFi^mF`bp7$$\"+'oP:Q%Fi^mFebp7%7$$\"++#yz^%Fi^mF[bp7$$\"+Wl\"*RYF i^mF`bp7$$\"+-S1#f%Fi^mFebp7%7$$\"+;X]GZFi^mF[bp7$$\"+gGW][Fi^mF`bp7$$ \"+=.f-[Fi^mFebp7%7$$\"+K3.R\\Fi^mF[bp7$$\"+w\"p41&Fi^mF`bp7$$\"+Mm68] Fi^mFebp7%7$$\"+1lRh$*Fe^m$\"+^iZ%[\"Fi^m7$$\"+\\.'Q1\"Fi^m$\"+H`:o:Fi ^m7$$\"+P#)G:5Fi^m$\"+@3-e:Fi^m7%7$$\"+nfmY6Fi^mFi^q7$$\"+lmQu7Fi^mF^_ q7$$\"+`X\"eA\"Fi^mFc_q7%7$$\"+$G#>d8Fi^mFi^q7$$\"+\")H\"\\[\"Fi^mF^_q 7$$\"+p3MO9Fi^mFc_q7%7$$\"+*f=xc\"Fi^mFi^q7$$\"+(HRap\"Fi^mF^_q7$$\"+& =nok\"Fi^mFc_q7%7$$\"+:\\CyFi^mF^_q7$$\"+,NRd=Fi^ mFc_q7%7$$\"+J7x))>Fi^mFi^q7$$\"+H>\\;@Fi^mF^_q7$$\"+<)>z1#Fi^mFc_q7%7 $$\"+ZvH*>#Fi^mFi^q7$$\"+X#=qK#Fi^mF^_q7$$\"+LhWyAFi^mFc_q7%7$$\"+jQ#) 4CFi^mFi^q7$$\"+hXaPDFi^mF^_q7$$\"+\\C(*)[#Fi^mFc_q7%7$$\"+z,N?EFi^mFi ^q7$$\"+x32[FFi^mF^_q7$$\"+l()\\*p#Fi^mFc_q7%7$$\"+&\\w3$GFi^mFi^q7$$ \"+$>(feHFi^mF^_q7$$\"+\"3D+\"HFi^mFc_q7%7$$\"+6GSTIFi^mFi^q7$$\"+4N7p JFi^mF^_q7$$\"+(R^07$Fi^mFc_q7%7$$\"+F\"H>D$Fi^mFi^q7$$\"+D)\\'zLFi^mF ^_q7$$\"+8x2JLFi^mFc_q7%7$$\"+VaXiMFi^mFi^q7$$\"+Thw/[Fi^mFc_q7%7$$\"+b'Rh$\\Fi^mFi^q7$$\"+`.'Q1&Fi^mF^_q7 $$\"+T#)G:]Fi^mFc_q7%7$$\"+XMgM$*Fe^m$\"+zlz!f\"Fi^m7$$\"+c'Rl1\"Fi^m$ \"+=8Os;Fi^m7$$\"+bfL<5Fi^m$\"+\"\\>Im\"Fi^m7%7$$\"+gm)R9\"Fi^mFg[r7$$ \"+sf1x7Fi^mF\\\\r7$$\"+rA'yA\"Fi^mFa\\r7%7$$\"+wH^a8Fi^mFg[r7$$\"+)G# f([\"Fi^mF\\\\r7$$\"+(e)QQ9Fi^mFa\\r7%7$$\"+#HR]c\"Fi^mFg[r7$$\"+/'=\" )p\"Fi^mF\\\\r7$$\"+.\\\"*[;Fi^mFa\\r7%7$$\"+3ccv Fi^mF\\\\r7$$\"+>7Wf=Fi^mFa\\r7%7$$\"+C>4')>Fi^mFg[r7$$\"+O7<>@Fi^mF\\ \\r7$$\"+Nv'*p?Fi^mFa\\r7%7$$\"+S#=m>#Fi^mFg[r7$$\"+_vpHBFi^mF\\\\r7$$ \"+^Q\\!G#Fi^mFa\\r7%7$$\"+cX92CFi^mFg[r7$$\"+oQASDFi^mF\\\\r7$$\"+n,- \"\\#Fi^mFa\\r7%7$$\"+s3nGGFi^mFg[r7$$\"++lFhHFi^mF\\\\r7$$\"+*zs?\"HFi^mFa \\r7%7$$\"+/NsQIFi^mFg[r7$$\"+;G!=<$Fi^mF\\\\r7$$\"+:\"*fAJFi^mFa\\r7% 7$$\"+?)\\#\\KFi^mFg[r7$$\"+K\"HBQ$Fi^mF\\\\r7$$\"+Ja7LLFi^mFa\\r7%7$$ \"+OhxfMFi^mFg[r7$$\"+[a&Gf$Fi^mF\\\\r7$$\"+Z!p5Fi^m$ \"+\"p!ew5Fi^m$\"+N3+oH%3l\"Fi^mF_ir7%7$$\"+;c3tFi^mFjhr7$$\"+N#p8 '=Fi^mF_ir7%7$$\"+K>h$)>Fi^mFehr7$$\"+G7l@@Fi^mFjhr7$$\"+^b*=2#Fi^mF_i r7%7$$\"+[#QT>#Fi^mFehr7$$\"+Wv:EFi^ mFehr7$$\"+w,B`FFi^mFjhr7$$\"+*\\uMq#Fi^mF_ir7%7$$\"+'>!p]Fi^mFjh r7$$\"+vRE>]Fi^mF_ir7%7$$\"+Fw'oG*Fe^m$\"+kBR.=Fi^m7$$\"+PKJr5Fi^m$\"+ k\"=3)=Fi^m7$$\"+\\s2@5Fi^m$\"+T\"pH(=Fi^m7%7$$\"+zI@R6Fi^mFces7$$\"+` &R=G\"Fi^mFhes7$$\"+lNgJ7Fi^mF]fs7%7$$\"+&RR(\\8Fi^mFces7$$\"+peO#\\\" Fi^mFhes7$$\"+\"))H@W\"Fi^mF]fs7%7$$\"+6dEg:Fi^mFces7$$\"+&=#*Gq\"Fi^m Fhes7$$\"+(>cEl\"Fi^mF]fs7%7$$\"+F?zqFi^mFhes7$$ \"+8D=j=Fi^mF]fs7%7$$\"+V$=8)>Fi^mFces7$$\"+<[%R7#Fi^mFhes7$$\"+H)3P2# Fi^mF]fs7%7$$\"+fY%=>#Fi^mFces7$$\"+L6ZMBFi^mFhes7$$\"+X^B%G#Fi^mF]fs7 %7$$\"+v4P-CFi^mFces7$$\"+\\u*\\a#Fi^mFhes7$$\"+h9w%\\#Fi^mF]fs7%7$$\" +\"H(*Gh#Fi^mFces7$$\"+lP_bFFi^mFhes7$$\"+xxG0FFi^mF]fs7%7$$\"+2OUBGFi ^mFces7$$\"+\"3]g'HFi^mFhes7$$\"+$49e\"HFi^mF]fs7%7$$\"+B*\\R.$Fi^mFce s7$$\"+(Rwl<$Fi^mFhes7$$\"+4/MEJFi^mF]fs7%7$$\"+RiZWKFi^mFces7$$\"+8F5 (Q$Fi^mFhes7$$\"+Dn'oL$Fi^mF]fs7%7$$\"+bD+bMFi^mFces7$$\"+H!Hwf$Fi^mFh es7$$\"+TIRZNFi^mF]fs7%7$$\"+r)Gbm$Fi^mFces7$$\"+X`:3QFi^mFhes7$$\"+d$ >zv$Fi^mF]fs7%7$$\"+(=bg(QFi^mFces7$$\"+h;o=SFi^mFhes7$$\"+tcWoRFi^mF] fs7%7$$\"+.:e'3%Fi^mFces7$$\"+xz?HUFi^mFhes7$$\"+*)>(*yTFi^mF]fs7%7$$ \"+>y5(H%Fi^mFces7$$\"+$HM(RWFi^mFhes7$$\"+0$)\\*Q%Fi^mF]fs7%7$$\"+NTj 2XFi^mFces7$$\"+41E]YFi^mFhes7$$\"+@Y-+YFi^mF]fs7%7$$\"+^/;=ZFi^mFces7 $$\"+Dpyg[Fi^mFhes7$$\"+P4b5[Fi^mF]fs7%7$$\"+nnoG\\Fi^mFces7$$\"+TKJr] Fi^mFhes7$$\"+`s2@]Fi^mF]fs7%7$$\"+\\mml#*Fe^m$\"+7%f'4>Fi^m7$$\"+NLVt 5Fi^m$\"+Ku2&)>Fi^m7$$\"+j7yA5Fi^m$\"+>\"Gz(>Fi^m7%7$$\"+\")H4P6Fi^mFa bt7$$\"+^'fRG\"Fi^mFfbt7$$\"+zvIL7Fi^mF[ct7%7$$\"+(H>wM\"Fi^mFabt7$$\" +nf[%\\\"Fi^mFfbt7$$\"+&*Q$QW\"Fi^mF[ct7%7$$\"+8c9e:Fi^mFabt7$$\"+$G7] q\"Fi^mFfbt7$$\"+6-Oa;Fi^mF[ct7%7$$\"+H>noFi^mFf bt7$$\"+Fl)['=Fi^mF[ct7%7$$\"+X#)>z>Fi^mFabt7$$\"+:\\1E@Fi^mFfbt7$$\"+ VGTv?Fi^mF[ct7%7$$\"+hXs*=#Fi^mFabt7$$\"+J7fOBFi^mFfbt7$$\"+f\"RfG#Fi^ mF[ct7%7$$\"+x3D+CFi^mFabt7$$\"+Zv6ZDFi^mFfbt7$$\"+vaY'\\#Fi^mF[ct7%7$ $\"+$>x2h#Fi^mFabt7$$\"+jQkdFFi^mFfbt7$$\"+\"z\"*pq#Fi^mF[ct7%7$$\"+4N I@GFi^mFabt7$$\"+z,B?\"R%Fi^mF[ct 7%7$$\"+PS^0XFi^mFabt7$$\"+22Q_YFi^mFfbt7$$\"+N'GFi^mFd_u7$$\"+Uq[m=Fi^mFi_u7%7$$\"+#**Qs(>Fi^mF__u7$$\"+oT-G@Fi^mF d_u7$$\"+eL,x?Fi^mFi_u7%7$$\"+3`w(=#Fi^mF__u7$$\"+%[]&QBFi^mFd_u7$$\"+ u'RvG#Fi^mFi_u7%7$$\"+C;H)R#Fi^mF__u7$$\"++o2\\DFi^mFd_u7$$\"+!*f1)\\# Fi^mFi_u7%7$$\"+Sz\")3EFi^mF__u7$$\"+;JgfFFi^mFd_u7$$\"+1Bf3FFi^mFi_u7 %7$$\"+cUM>GFi^mF__u7$$\"+K%H,(HFi^mFd_u7$$\"+A'=\">HFi^mFi_u7%7$$\"+s 0()HIFi^mF__u7$$\"+[dl!=$Fi^mFd_u7$$\"+Q\\kHJFi^mFi_u7%7$$\"+))oRSKFi^ mF__u7$$\"+k?=\"R$Fi^mFd_u7$$\"+a7(QFi^mF__u7$$\"+75wASFi^mFd _u7$$\"+--vrRFi^mFi_u7%7$$\"+_@]#3%Fi^mF__u7$$\"+GtGLUFi^mFd_u7$$\"+=l F#=%Fi^mFi_u7%7$$\"+o%GIH%Fi^mF__u7$$\"+WO\"QW%Fi^mFd_u7$$\"+MG!GR%Fi^ mFi_u7%7$$\"+%yaN]%Fi^mF__u7$$\"+g*RVl%Fi^mFd_u7$$\"+]\"HLg%Fi^mFi_u7% 7$$\"++639ZFi^mF__u7$$\"+wi'['[Fi^mFd_u7$$\"+ma&Q\"[Fi^mFi_u7%7$$\"+;u gC\\Fi^mF__u7$$\"+#f#Rv]Fi^mFd_u7$$\"+#y\"QC]Fi^mFi_u7%7$$\"+4\"ozA*Fe ^m$\"+]w6A@Fi^m7$$\"+*=.s2\"Fi^m$\"+E=n$>#Fi^m7$$\"+%o%)e-\"Fi^m$\"+\" HIy=#Fi^m7%7$$\"+FJKL6Fi^mF]\\v7$$\"+0&HxG\"Fi^mFb\\v7$$\"++5TO7Fi^mFg \\v7%7$$\"+V%\\QM\"Fi^mF]\\v7$$\"+@eD)\\\"Fi^mFb\\v7$$\"+;t$pW\"Fi^mFg \\v7%7$$\"+fdPa:Fi^mF]\\v7$$\"+P@y3>Fi^mFb\\v7$$\"+[**)z'=Fi^mFg\\v7%7$$\" +\"RGa(>Fi^mF]\\v7$$\"+pZ$)H@Fi^mFb\\v7$$\"+ki^y?Fi^mFg\\v7%7$$\"+2Z&f =#Fi^mF]\\v7$$\"+&3h.M#Fi^mFb\\v7$$\"+!eU!*G#Fi^mFg\\v7%7$$\"+B5['R#Fi ^mF]\\v7$$\"+,u)3b#Fi^mFb\\v7$$\"+'*)o&*\\#Fi^mFg\\v7%7$$\"+Rt+2EFi^mF ]\\v7$$\"+(HFi^mFb\\v7$$\"+G:i?HFi^mFg\\v7%7$$\"+r*f!GIFi^mF]\\v7$$\"+\\j Y#=$Fi^mFb\\v7$$\"+Wy9JJFi^mFg\\v7%7$$\"+(G'eQKFi^mF]\\v7$$\"+lE*HR$Fi ^mFb\\v7$$\"+gTnTLFi^mFg\\v7%7$$\"+.E6\\MFi^mF]\\v7$$\"+\")*=Ng$Fi^mFb \\v7$$\"+w/?_NFi^mFg\\v7%7$$\"+>*Q'fOFi^mF]\\v7$$\"+(HXS\"QFi^mFb\\v7$ $\"+#zEFw$Fi^mFg\\v7%7$$\"+N_;qQFi^mF]\\v7$$\"+8;dCSFi^mFb\\v7$$\"+3JD tRFi^mFg\\v7%7$$\"+^:p!3%Fi^mF]\\v7$$\"+Hz4NUFi^mFb\\v7$$\"+C%zP=%Fi^m Fg\\v7%7$$\"+ny@\"H%Fi^mF]\\v7$$\"+XUiXWFi^mFb\\v7$$\"+SdI%R%Fi^mFg\\v 7%7$$\"+$=W<]%Fi^mF]\\v7$$\"+h0:cYFi^mFb\\v7$$\"+c?$[g%Fi^mFg\\v7%7$$ \"+*\\qAr%Fi^mF]\\v7$$\"+xonm[Fi^mFb\\v7$$\"+s$e`\"[Fi^mFg\\v7%7$$\"+: ozA\\Fi^mF]\\v7$$\"+$>.s2&Fi^mFb\\v7$$\"+)o%)e-&Fi^mFg\\v7%7$$\"+TDB6# *Fe^m$\"+!Q0$GAFi^m7$$\"+Yn()y5Fi^m$\"+7/,)H#Fi^m7$$\"+beHF5Fi^m$\"+B% yFH#Fi^m7%7$$\"+q&\\;8\"Fi^mF[iv7$$\"+iIS*G\"Fi^mF`iv7$$\"+r@#yB\"Fi^m Feiv7%7$$\"+')eFi^mF`iv7$$\"+>6Sp=Fi^mFeiv7%7$$\"+M[vt>Fi^m F[iv7$$\"+E$3:8#Fi^mF`iv7$$\"+Nu#*z?Fi^mFeiv7%7$$\"+]6G%=#Fi^mF[iv7$$ \"+UY.UBFi^mF`iv7$$\"+^PX!H#Fi^mFeiv7%7$$\"+mu![R#Fi^mF[iv7$$\"+e4c_DF i^mF`iv7$$\"+n+)4]#Fi^mFeiv7%7$$\"+#yL`g#Fi^mF[iv7$$\"+us3jFFi^mF`iv7$ $\"+$Q1:r#Fi^mFeiv7%7$$\"+)4ge\"GFi^mF[iv7$$\"+!f8O(HFi^mF`iv7$$\"+*pK ?#HFi^mFeiv7%7$$\"+9kQEIFi^mF[iv7$$\"+1*RT=$Fi^mF`iv7$$\"+:!fD8$Fi^mFe iv7%7$$\"+IF\"pB$Fi^mF[iv7$$\"+Aim%R$Fi^mF`iv7$$\"+J`3VLFi^mFeiv7%7$$ \"+Y!RuW$Fi^mF[iv7$$\"+QD>0OFi^mF`iv7$$\"+Z;h`NFi^mFeiv7%7$$\"+i`'zl$F i^mF[iv7$$\"+a)=d\"QFi^mF`iv7$$\"+jz8kPFi^mFeiv7%7$$\"+y;\\oQFi^mF[iv7 $$\"+q^CESFi^mF`iv7$$\"+zUmuRFi^mFeiv7%7$$\"+%*z,zSFi^mF[iv7$$\"+'[rnB %Fi^mF`iv7$$\"+&f!>&=%Fi^mFeiv7%7$$\"+5Va*G%Fi^mF[iv7$$\"+-yHZWFi^mF`i v7$$\"+6pr&R%Fi^mFeiv7%7$$\"+E12+XFi^mF[iv7$$\"+=T#yl%Fi^mF`iv7$$\"+FK C1YFi^mFeiv7%7$$\"+Upf5ZFi^mF[iv7$$\"+M/No[Fi^mF`iv7$$\"+V&pn\"[Fi^mFe iv7%7$$\"+eK7@\\Fi^mF[iv7$$\"+]n()y]Fi^mF`iv7$$\"+feHF]Fi^mFeiv7%7$$\" +$)zv&>*Fe^m$\"+pTYMBFi^m7$$\"+-UU!3\"Fi^m$\"+RzP-CFi^m7$$\"+f5iG5Fi^m $\"+-ss(R#Fi^m7%7$$\"+9@5I6Fi^mFiew7$$\"+=0&4H\"Fi^mF^fw7$$\"+vt9R7Fi^ mFcfw7%7$$\"+I%G1M\"Fi^mFiew7$$\"+MoZ,:Fi^mF^fw7$$\"+\"pt'\\9Fi^mFcfw7 %7$$\"+YZ:^:Fi^mFiew7$$\"+]J+7Fi^mF^fw7$$\"+Bjsq=Fi^mFcfw7%7$$\"+yt?s>Fi^mFiew7 $$\"+#ybI8#Fi^mF^fw7$$\"+RED\"3#Fi^mFcfw7%7$$\"+%pLF=#Fi^mFiew7$$\"+)4 #eVBFi^mF^fw7$$\"+b*yU)Q8$Fi^mFcfw7%7$$ \"+u_ONKFi^mFiew7$$\"+yO@'R$Fi^mF^fw7$$\"+N0TWLFi^mFcfw7%7$$\"+!f\"*eW $Fi^mFiew7$$\"+%**Rng$Fi^mF^fw7$$\"+^o$\\b$Fi^mFcfw7%7$$\"+1zTcOFi^mFi ew7$$\"+5jE\\Fi^mFiew7$$\"+1UU!3&Fi^mF^fw7$$\"+j5iG]Fi^mFcfw7%7$$\"+x ?W\"=*Fe^m$\"+tNfSCFi^m7$$\"+#zb=3\"Fi^m$\"+^[x1DFi^m7$$\"+ue')H5Fi^m$ \"+e\"yE]#Fi^m7%7$$\"+C0nG6Fi^mFgbx7$$\"+3@Q#H\"Fi^mF\\cx7$$\"+!>#RS7F i^mFacx7%7$$\"+So>R8Fi^mFgbx7$$\"+C%3H]\"Fi^mF\\cx7$$\"+1&=4X\"Fi^mFac x7%7$$\"+cJs\\:Fi^mFgbx7$$\"+SZV8Fi^mF\\cx7$$\"+Q6(>(=Fi^mFacx7%7$$\"+)yv2( >Fi^mFgbx7$$\"+st[M@Fi^mF\\cx7$$\"+au\\#3#Fi^mFacx7%7$$\"+/@I\"=#Fi^mF gbx7$$\"+)o8]M#Fi^mF\\cx7$$\"+qP-$H#Fi^mFacx7%7$$\"+?%G=R#Fi^mFgbx7$$ \"+/+abDFi^mF\\cx7$$\"+'3]N]#Fi^mFacx7%7$$\"+OZN-EFi^mFgbx7$$\"+?j1mFF i^mF\\cx7$$\"+-k29FFi^mFacx7%7$$\"+_5)G\"GFi^mFgbx7$$\"+OEfwHFi^mF\\cx 7$$\"+=FgCHFi^mFacx7%7$$\"+otSBIFi^mFgbx7$$\"+_*=r=$Fi^mF\\cx7$$\"+M!H ^8$Fi^mFacx7%7$$\"+%oLRB$Fi^mFgbx7$$\"+o_k(R$Fi^mF\\cx7$$\"+]`lXLFi^mF acx7%7$$\"+++YWMFi^mFgbx7$$\"+%er\"3OFi^mF\\cx7$$\"+m;=cNFi^mFacx7%7$$ \"+;j)\\l$Fi^mFgbx7$$\"++zp=QFi^mF\\cx7$$\"+#)zqmPFi^mFacx7%7$$\"+KE^l QFi^mFgbx7$$\"+;UAHSFi^mF\\cx7$$\"+)HMs(RFi^mFacx7%7$$\"+[*Qg2%Fi^mFgb x7$$\"+K0vRUFi^mF\\cx7$$\"+91w(=%Fi^mFacx7%7$$\"+k_c'G%Fi^mFgbx7$$\"+[ oF]WFi^mF\\cx7$$\"+IpG)R%Fi^mFacx7%7$$\"+!e\"4(\\%Fi^mFgbx7$$\"+kJ!3m% Fi^mF\\cx7$$\"+YK\")3YFi^mFacx7%7$$\"+'*yh2ZFi^mFgbx7$$\"+![H8([Fi^mF \\cx7$$\"+i&R$>[Fi^mFacx7%7$$\"+7U9=\\Fi^mFgbx7$$\"+'zb=3&Fi^mF\\cx7$$ \"+ye')H]Fi^mFacx7%7$$\"+$o*=o\"*Fe^m$\"+,NpYDFi^m7$$\"+K5=$3\"Fi^m$\" +R7?6EFi^m7$$\"+ac.J5Fi^m$\"+LDj2EFi^m7%7$$\"+%GXt7\"Fi^mFe_y7$$\"+[tq $H\"Fi^mFj_y7$$\"+q>cT7Fi^mF_`y7%7$$\"++;(yL\"Fi^mFe_y7$$\"+kOB/:Fi^mF j_y7$$\"+'G)3_9Fi^mF_`y7%7$$\"+;zR[:Fi^mFe_y7$$\"+!)*fZr\"Fi^mFj_y7$$ \"+-Yhi;Fi^mF_`y7%7$$\"+KU#*eFi^mFj_y7$$\"+=49t=F i^mF_`y7%7$$\"+[0Xp>Fi^mFe_y7$$\"+7E\"e8#Fi^mFj_y7$$\"+Msm$3#Fi^mF_`y7 %7$$\"+ko(*z@Fi^mFe_y7$$\"+G*QjM#Fi^mFj_y7$$\"+]N>%H#Fi^mF_`y7%7$$\"+! =.0R#Fi^mFe_y7$$\"+W_'ob#Fi^mFj_y7$$\"+m)>Z]#Fi^mF_`y7%7$$\"+'\\H5g#Fi ^mFe_y7$$\"+g:RnFFi^mFj_y7$$\"+#=Y_r#Fi^mF_`y7%7$$\"+7eb6GFi^mFe_y7$$ \"+wy\"z(HFi^mFj_y7$$\"+)\\sd#HFi^mF_`y7%7$$\"+G@3AIFi^mFe_y7$$\"+#>W% )=$Fi^mFj_y7$$\"+9))HOJFi^mF_`y7%7$$\"+W%3EB$Fi^mFe_y7$$\"+30(*)R$Fi^m Fj_y7$$\"+I^#oM$Fi^mF_`y7%7$$\"+gZ8VMFi^mFe_y7$$\"+Co\\4OFi^mFj_y7$$\" +Y9NdNFi^mF_`y7%7$$\"+w5m`OFi^mFe_y7$$\"+SJ-?QFi^mFj_y7$$\"+ix(yw$Fi^m F_`y7%7$$\"+#R(=kQFi^mFe_y7$$\"+c%\\0.%Fi^mFj_y7$$\"+ySSyRFi^mF_`y7%7$ $\"+3PruSFi^mFe_y7$$\"+sd2TUFi^mFj_y7$$\"+%RI*)=%Fi^mF_`y7%7$$\"+C+C&G %Fi^mFe_y7$$\"+)3-;X%Fi^mFj_y7$$\"+5nX*R%Fi^mF_`y7%7$$\"+Sjw&\\%Fi^mFe _y7$$\"+/%G@m%Fi^mFj_y7$$\"+EI)*4YFi^mF_`y7%7$$\"+cEH1ZFi^mFe_y7$$\"+? Zls[Fi^mFj_y7$$\"+U$40#[Fi^mF_`y7%7$$\"+s*=o\"\\Fi^mFe_y7$$\"+O5=$3&Fi ^mFj_y7$$\"+ec.J]Fi^mF_`y7%7$$\"+8G\"f:*Fe^m$\"+VTw_EFi^m7$$\"+>(3W3\" Fi^m$\"+8pl:FFi^m7$$\"+za8K5Fi^m$\"+>8f7FFi^m7%7$$\"+(fFi^mFh \\z7$$\"+V2Cu=Fi^mF]]z7%7$$\"+hGAo>Fi^mFc\\z7$$\"+*HSq8#Fi^mFh\\z7$$\" +fqw%3#Fi^mF]]z7%7$$\"+x\"\\(y@Fi^mFc\\z7$$\"+:mcZBFi^mFh\\z7$$\"+vLH& H#Fi^mF]]z7%7$$\"+$\\v#*Q#Fi^mFc\\z7$$\"+JH4eDFi^mFh\\z7$$\"+\"p>e]#Fi ^mF]]z7%7$$\"+4=!)*f#Fi^mFc\\z7$$\"+Z#>'oFFi^mFh\\z7$$\"+2gM;FFi^mF]]z 7%7$$\"+D\"G.\"GFi^mFc\\z7$$\"+jb9zHFi^mFh\\z7$$\"+BB(o#HFi^mF]]z7%7$$ \"+TW&3-$Fi^mFc\\z7$$\"+z=n*=$Fi^mFh\\z7$$\"+R')RPJFi^mF]]z7%7$$\"+d2Q JKFi^mFc\\z7$$\"+&>)>+MFi^mFh\\z7$$\"+b\\#zM$Fi^mF]]z7%7$$\"+tq!>W$Fi^ mFc\\z7$$\"+6Xs5OFi^mFh\\z7$$\"+r7XeNFi^mF]]z7%7$$\"+*QLCl$Fi^mFc\\z7$ $\"+F3D@QFi^mFh\\z7$$\"+(ex*oPFi^mF]]z7%7$$\"+0(fH'QFi^mFc\\z7$$\"+Vrx JSFi^mFh\\z7$$\"+.R]zRFi^mF]]z7%7$$\"+@g[tSFi^mFc\\z7$$\"+fMIUUFi^mFh \\z7$$\"+>-.!>%Fi^mF]]z7%7$$\"+PB,%G%Fi^mFc\\z7$$\"+v(HGX%Fi^mFh\\z7$$ \"+Nlb+WFi^mF]]z7%7$$\"+`'QX\\%Fi^mFc\\z7$$\"+\"4cLm%Fi^mFh\\z7$$\"+^G 36YFi^mF]]z7%7$$\"+p\\10ZFi^mFc\\z7$$\"+2C)Q([Fi^mFh\\z7$$\"+n\"4;#[Fi ^mF]]z7%7$$\"+&G\"f:\\Fi^mFc\\z7$$\"+B(3W3&Fi^mFh\\z7$$\"+$[N@.&Fi^mF] ]z7%7$$\"+;/`W\"*Fe^m$\"+3f!)eFFi^m7$$\"+epa&3\"Fi^m$\"+k99?GFi^m7$$\" +],.Y:Fi^mFaiz7$$\"+1f7<Fi^mFfiz7$$\"+9aFv=Fi^mF[jz7%7$$ \"+AY3n>Fi^mFaiz7$$\"+Q&y\"Q@Fi^mFfiz7$$\"+IIFi^mFaiz7$$\"+=,\"3>$Fi^mFfiz7$$\" +5LVQJFi^mF[jz7%7$$\"+=DCIKFi^mFaiz7$$\"+MkL,MFi^mFfiz7$$\"+E'f*[LFi^m F[jz7%7$$\"+M)o2W$Fi^mFaiz7$$\"+]F'=h$Fi^mFfiz7$$\"+Uf[fNFi^mF[jz7%7$$ \"+]^H^OFi^mFaiz7$$\"+m!*QAQFi^mFfiz7$$\"+eA,qPFi^mF[jz7%7$$\"+m9#='QF i^mFaiz7$$\"+#Q:H.%Fi^mFfiz7$$\"+u&Q0)RFi^mF[jz7%7$$\"+#yZB2%Fi^mFaiz7 $$\"+)pTMC%Fi^mFfiz7$$\"+!*[1\">%Fi^mF[jz7%7$$\"+)4uGG%Fi^mFaiz7$$\"+9 !oRX%Fi^mFfiz7$$\"+17f,WFi^mF[jz7%7$$\"+9/S$\\%Fi^mFaiz7$$\"+IV\\kYFi^ mFfiz7$$\"+Av67YFi^mF[jz7%7$$\"+In#Rq%Fi^mFaiz7$$\"+Y1-v[Fi^mFfiz7$$\" +QQkA[Fi^mF[jz7%7$$\"+YIX9\\Fi^mFaiz7$$\"+ipa&3&Fi^mFfiz7$$\"+a,['GFi^m7$$\"+%>.m3\"Fi^m$\"+6VlCHFi^m7$$ \"+yT9M5Fi^m$\"+n]_AHFi^m7%7$$\"+BJ#R7\"Fi^mF_f[l7$$\"+5&HrH\"Fi^mFdf[ l7$$\"+%\\qYC\"Fi^mFif[l7%7$$\"+R%\\WL\"Fi^mF_f[l7$$\"+Eel2:Fi^mFdf[l7 $$\"+5o>b9Fi^mFif[l7%7$$\"+bd(\\a\"Fi^mF_f[l7$$\"+U@==Fi^mFdf[l7$$\"+U%\\i(= Fi^mFif[l7%7$$\"+(QGg'>Fi^mF_f[l7$$\"+uZBR@Fi^mFdf[l7$$\"+edx'3#Fi^mFi f[l7%7$$\"+.Zbw@Fi^mF_f[l7$$\"+!4h(\\BFi^mFdf[l7$$\"+u?I(H#Fi^mFif[l7% 7$$\"+>53(Q#Fi^mF_f[l7$$\"+1uGgDFi^mFdf[l7$$\"+!RGy]#Fi^mFif[l7%7$$\"+ Ntg(f#Fi^mF_f[l7$$\"+AP\"3x#Fi^mFdf[l7$$\"+1ZN=FFi^mFif[l7%7$$\"+^O83G Fi^mF_f[l7$$\"+Q+M\")HFi^mFdf[l7$$\"+A5))GHFi^mFif[l7%7$$\"+n*f'=IFi^m F_f[l7$$\"+aj'=>$Fi^mFdf[l7$$\"+QtSRJFi^mFif[l7%7$$\"+$G'=HKFi^mF_f[l7 $$\"+qER-MFi^mFdf[l7$$\"+aO$*\\LFi^mFif[l7%7$$\"+*f7(RMFi^mF_f[l7$$\"+ ')*=Hh$Fi^mFdf[l7$$\"+q*f/c$Fi^mFif[l7%7$$\"+:*Q-l$Fi^mF_f[l7$$\"+-`WB QFi^mFdf[l7$$\"+'G')4x$Fi^mFif[l7%7$$\"+J_wgQFi^mF_f[l7$$\"+=;(R.%Fi^m Fdf[l7$$\"+-E^\")RFi^mFif[l7%7$$\"+Z:HrSFi^mF_f[l7$$\"+Mz\\WUFi^mFdf[l 7$$\"+=*Q?>%Fi^mFif[l7%7$$\"+jy\"=G%Fi^mF_f[l7$$\"+]U-bWFi^mFdf[l7$$\" +M_c-WFi^mFif[l7%7$$\"+zTM#\\%Fi^mF_f[l7$$\"+m0blYFi^mFdf[l7$$\"+]:48Y Fi^mFif[l7%7$$\"+&\\qGq%Fi^mF_f[l7$$\"+#)o2w[Fi^mFdf[l7$$\"+myhB[Fi^mF if[l7%7$$\"+6oR8\\Fi^mF_f[l7$$\"+)>.m3&Fi^mFdf[l7$$\"+#=WT.&Fi^mFif[l7 %7$$\"+&edT7*Fe^m$\"+b_!3(HFi^m7$$\"+UUe(3\"Fi^m$\"+\\Z>HIFi^m7$$\"+z< 1N5Fi^m$\"+$3,v-$Fi^m7%7$$\"+u?%H7\"Fi^mF]c\\l7$$\"+e06)H\"Fi^mFbc\\l7 $$\"+&4)eX7Fi^mFgc\\l7%7$$\"+!RoML\"Fi^mF]c\\l7$$\"+uoj3:Fi^mFbc\\l7$$ \"+6W6c9Fi^mFgc\\l7%7$$\"+1Z*Ra\"Fi^mF]c\\l7$$\"+!>j\">Fi^mFbc\\l7$$\"+V q;x=Fi^mFgc\\l7%7$$\"+Qt/l>Fi^mF]c\\l7$$\"+Ae@S@Fi^mFbc\\l7$$\"+fLp(3# Fi^mFgc\\l7%7$$\"+aOdv@Fi^mF]c\\l7$$\"+Q@u]BFi^mFbc\\l7$$\"+v'>#)H#Fi^ mFgc\\l7%7$$\"+q**4'Q#Fi^mF]c\\l7$$\"+a%o7c#Fi^mFbc\\l7$$\"+\"*fu3DFi^ mFgc\\l7%7$$\"+'GEmf#Fi^mF]c\\l7$$\"+qZzrFFi^mFbc\\l7$$\"+2BF>FFi^mFgc \\l7%7$$\"+-E:2GFi^mF]c\\l7$$\"+'3@B)HFi^mFbc\\l7$$\"+B')zHHFi^mFgc\\l 7%7$$\"+=*yw,$Fi^mF]c\\l7$$\"+-u%G>$Fi^mFbc\\l7$$\"+R\\KSJFi^mFgc\\l7% 7$$\"+M_?GKFi^mF]c\\l7$$\"+=PP.MFi^mFbc\\l7$$\"+b7&3N$Fi^mFgc\\l7%7$$ \"+]:tQMFi^mF]c\\l7$$\"+M+!Rh$Fi^mFbc\\l7$$\"+rvPhNFi^mFgc\\l7%7$$\"+m yD\\OFi^mF]c\\l7$$\"+]jUCQFi^mFbc\\l7$$\"+()Q!>x$Fi^mFgc\\l7%7$$\"+#=% yfQFi^mF]c\\l7$$\"+mE&\\.%Fi^mFbc\\l7$$\"+.-V#)RFi^mFgc\\l7%7$$\"+)\\5 .2%Fi^mF]c\\l7$$\"+#)*yaC%Fi^mFbc\\l7$$\"+>l&H>%Fi^mFgc\\l7%7$$\"+9o$3 G%Fi^mF]c\\l7$$\"+)H0gX%Fi^mFbc\\l7$$\"+NG[.WFi^mFgc\\l7%7$$\"+IJO\"\\ %Fi^mF]c\\l7$$\"+9;`mYFi^mFbc\\l7$$\"+^\"4Sh%Fi^mFgc\\l7%7$$\"+Y%*)=q% Fi^mF]c\\l7$$\"+Iz0x[Fi^mFbc\\l7$$\"+na`C[Fi^mFgc\\l7%7$$\"+idT7\\Fi^m F]c\\l7$$\"+YUe(3&Fi^mFbc\\l7$$\"+$yh].&Fi^mFgc\\l-Fe]m6&Fg]m$\")=THvF j]mFi_]lFi_]l-%+AXESLABELSG6$%\"xG%\"yG-%%VIEWG6$;$\"+++++!)Fe^m$\"+++ ++_Fi^m;$\"+++++!*Fe^m$\"+++++JFi^m" 2 492 363 363 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 483 14 "Sixth Example:" }{TEXT -1 2 "\n\n" }{TEXT 485 66 "A differential equation of Bernoulli type t hat is also separable. " }{TEXT -1 1 "\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "ode := diff(y(x),x) = x/y(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG/-%%diffG6$-%\"yG6#%\"xGF,*&F,\"\"\"F)!\"\"" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Bernoulli_ode(ode);" }}{PARA 6 "" 1 "" {TEXT -1 53 "Switching to t ype [separable].\nCalling separable_ode:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%/-%%diffG6$-%\"yG6#%\"xGF+*&F+\"\"\"F(!\"\"/-%$IntG6$F)F),&-F1 6$F+F+F-%#_CGF-/,$*$F(\"\"##F-F:,&*$F+F:F;F6F-" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 489 16 "Seventh Example:" }{TEXT -1 2 "\n\n" }{TEXT 490 78 "A differen tial equation of Bernoulli type that is already linear (because " }{TEXT 491 5 "n = 0" }{TEXT 492 4 "). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "ode := diff(y(x),x) + y(x)/x = x;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$odeG/,&-%%diffG6$-%\"yG6#%\"xGF-\"\"\"*&F*F.F-!\" \"F.F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ic := y(1) = 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Bernoulli_ode(ode,ic);" } }{PARA 6 "" 1 "" {TEXT -1 45 "Equation is linear. Switching to type li near:" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7*/,&-%%diffG6$-%\"yG6#%\"xGF ,\"\"\"*&F)F-F,!\"\"F-F,/*&-%$expG6#-%$IntG6$*$F,F/F,F-F%F-*&F2F-F,F-/ -%%DiffG6$**%\"(GF-F2F-F)F-%\")GF-F,F9/*&F2F-F)F-,&-F66$F9F,F-%\"CGF-/ *&F,F-F)F-,&-F66$*$F,\"\"#F,F-FFF-/FH,&*$F,\"\"$#F-FQFFF-/F)*&F,F/FOF- /F)*&F,F/,&FP#F-FMF,#F/FMF-" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 487 32 "Copyright and Author Information" }} {EXCHG {PARA 261 "" 0 "" {TEXT -1 38 "1.6epR4.mws A MapleV R4 work sheet." }}{PARA 261 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 84 "Author: Brian E. Blank \nWritten: 19 September 1997\nLast R evised: 30 January 2001" }}{PARA 261 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 51 "This document may not be distributed by any medium ," }}{PARA 0 "" 0 "" {TEXT -1 55 "including print, disk, and electroni c transfer, without" }}{PARA 0 "" 0 "" {TEXT -1 39 "prior written perm ission of the author." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 49 "For more information, please contact the author:" } }{PARA 261 "" 0 "" {TEXT -1 4 " " }}{PARA 261 "" 0 "" {TEXT -1 5 " \+ " }{TEXT 495 25 "Department of Mathematics" }{TEXT -1 2 ", " }} {PARA 0 "" 0 "" {TEXT -1 39 " Washington University in St. Louis" }}{PARA 0 "" 0 "" {TEXT -1 26 " St. Louis, MO 63130" }}{PARA 0 " " 0 "" {TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 33 " Telephone: (314) 935-6763" }}{PARA 261 "" 0 "" {TEXT -1 44 " e-ma il: brian@math.wustl.edu" }}{PARA 261 "" 0 "" {TEXT -1 0 "" }} {PARA 261 "" 0 "" {TEXT -1 61 "Copyright: \251 1997-2001 Brian E. Bla nk, All Rights Reserved." }}}}}{MARK "8 1 17 0" 23 }{VIEWOPTS 1 1 0 1 1 1803 }