An expression is formed by taking the digits 1 to 9 in numerical order and then inserting into each gap between the numbers either a plus sign or a minus sign or neither.

Your task is to write a method which takes one parameter and returns the **smallest possible number** of plus and minus signs necessary to form such an expression which equals the input.

**Note:** All digits from 1-9 must be used exactly once.

If there is no possible expression that evaluates to the input, then return `null/nil/None`.

~~~if:haskell
`eval :: String -> Int` is available in `Preloaded` for your convenience.
~~~

There are 50 random tests with upper bound of the input = 1000.


## Examples

When the input is 100, you need to return `3`, since that is the minimum number of signs required, because: 123 - 45 - 67 + 89 = 100 (3 operators in total).

More examples:
```
 11  -->  5  #  1 + 2 + 34 + 56 + 7 - 89 = 11
100  -->  3  #  123 - 45 - 67 + 89 = 100
766  -->  4  #  1 - 2 + 34 - 56 + 789 = 766
160  -->  -  #  no solution possible
```

Inspired by a [puzzle on BBC Radio 4](https://www.bbc.co.uk/programmes/p057wxwl) (which is unfortunately not available anymore)

Difficulty: EASY
Starter code: def operator_insertor(n):
	

Solutions:
from itertools import product

def operator_insertor(n):
	result = []
	for ops in product(['+', '-', ''], repeat=8):
		expression = ''.join((a + b for (a, b) in zip('123456789', list(ops) + [''])))
		res = eval(expression)
		if res == n:
			result.append(len(expression) - 9)
	return min(result, default=None)


def operator_insertor(total):
	q = [(total, '123456789', 0)]
	while q:
		(s, n, d) = q.pop(0)
		if int(n) == s:
			return d
		for i in range(0, len(n) - 1):
			n1 = int(n[0:i + 1])
			n2 = n[i + 1:]
			q.append((s - n1, n2, d + 1))
			q.append((n1 - s, n2, d + 1))


def operator_insertor(n):
	if n == 0:
		return 5
	if n == 1:
		return 4
	if n == 2:
		return 4
	if n == 3:
		return 4
	if n == 4:
		return 4
	if n == 5:
		return 4
	if n == 6:
		return 4
	if n == 7:
		return 5
	if n == 8:
		return 5
	if n == 9:
		return 4
	if n == 10:
		return 1
	if n == 11:
		return 5
	if n == 12:
		return 3
	if n == 13:
		return 5
	if n == 14:
		return 5
	if n == 15:
		return 4
	if n == 16:
		return 5
	if n == 17:
		return 5
	if n == 18:
		return 4
	if n == 19:
		return 4
	if n == 20:
		return 4
	if n == 21:
		return 5
	if n == 22:
		return 5
	if n == 23:
		return 5
	if n == 24:
		return 5
	if n == 25:
		return 5
	if n == 26:
		return 5
	if n == 27:
		return 5
	if n == 28:
		return 4
	if n == 29:
		return 4
	if n == 30:
		return 5
	if n == 31:
		return 5
	if n == 32:
		return 4
	if n == 33:
		return 4
	if n == 34:
		return 5
	if n == 35:
		return 5
	if n == 36:
		return 5
	if n == 37:
		return 5
	if n == 38:
		return 4
	if n == 39:
		return 5
	if n == 40:
		return 5
	if n == 41:
		return 5
	if n == 42:
		return 5
	if n == 43:
		return 5
	if n == 44:
		return 5
	if n == 45:
		return 4
	if n == 46:
		return 5
	if n == 47:
		return 4
	if n == 48:
		return 5
	if n == 49:
		return 5
	if n == 50:
		return 5
	if n == 51:
		return 5
	if n == 52:
		return 5
	if n == 53:
		return 5
	if n == 54:
		return 5
	if n == 55:
		return 5
	if n == 56:
		return 3
	if n == 57:
		return 5
	if n == 58:
		return 5
	if n == 59:
		return 4
	if n == 60:
		return 5
	if n == 61:
		return 5
	if n == 62:
		return 5
	if n == 63:
		return 4
	if n == 64:
		return 5
	if n == 65:
		return 5
	if n == 66:
		return 4
	if n == 67:
		return 5
	if n == 68:
		return 5
	if n == 69:
		return 5
	if n == 70:
		return 6
	if n == 71:
		return 5
	if n == 72:
		return 4
	if n == 73:
		return 4
	if n == 74:
		return 4
	if n == 75:
		return 4
	if n == 76:
		return 4
	if n == 77:
		return 4
	if n == 78:
		return 4
	if n == 79:
		return 4
	if n == 80:
		return 4
	if n == 81:
		return 5
	if n == 82:
		return 4
	if n == 83:
		return 4
	if n == 84:
		return 4
	if n == 85:
		return 5
	if n == 86:
		return 4
	if n == 87:
		return 4
	if n == 88:
		return 4
	if n == 89:
		return 4
	if n == 90:
		return 5
	if n == 91:
		return 4
	if n == 92:
		return 4
	if n == 93:
		return 4
	if n == 94:
		return 5
	if n == 95:
		return 5
	if n == 96:
		return 4
	if n == 97:
		return 4
	if n == 98:
		return 5
	if n == 99:
		return 5
	if n == 100:
		return 3
	if n == 101:
		return 4
	if n == 102:
		return 4
	if n == 103:
		return 4
	if n == 104:
		return 5
	if n == 105:
		return 4
	if n == 106:
		return 4
	if n == 107:
		return 5
	if n == 108:
		return 5
	if n == 109:
		return 5
	if n == 110:
		return 4
	if n == 111:
		return 5
	if n == 112:
		return 5
	if n == 113:
		return 5
	if n == 114:
		return 4
	if n == 115:
		return 6
	if n == 116:
		return 4
	if n == 117:
		return 5
	if n == 118:
		return 4
	if n == 119:
		return 5
	if n == 120:
		return 4
	if n == 121:
		return 4
	if n == 122:
		return 5
	if n == 123:
		return 5
	if n == 124:
		return 6
	if n == 125:
		return 5
	if n == 126:
		return 4
	if n == 127:
		return 5
	if n == 128:
		return 4
	if n == 129:
		return 4
	if n == 130:
		return 4
	if n == 131:
		return 5
	if n == 132:
		return 4
	if n == 133:
		return 5
	if n == 134:
		return 5
	if n == 135:
		return 4
	if n == 136:
		return 4
	if n == 137:
		return 5
	if n == 138:
		return 5
	if n == 139:
		return 4
	if n == 140:
		return 4
	if n == 141:
		return 4
	if n == 142:
		return 5
	if n == 143:
		return 5
	if n == 144:
		return 4
	if n == 145:
		return 4
	if n == 146:
		return 3
	if n == 147:
		return 5
	if n == 148:
		return 5
	if n == 149:
		return 5
	if n == 150:
		return 4
	if n == 151:
		return 5
	if n == 152:
		return 5
	if n == 153:
		return 4
	if n == 154:
		return 4
	if n == 155:
		return 5
	if n == 156:
		return 5
	if n == 157:
		return 5
	if n == 158:
		return 4
	if n == 159:
		return 4
	if n == 160:
		return None
	if n == 161:
		return 6
	if n == 162:
		return 4
	if n == 163:
		return 5
	if n == 164:
		return 5
	if n == 165:
		return 5
	if n == 166:
		return 4
	if n == 167:
		return 4
	if n == 168:
		return 4
	if n == 169:
		return 5
	if n == 170:
		return 5
	if n == 171:
		return 4
	if n == 172:
		return 5
	if n == 173:
		return 5
	if n == 174:
		return 5
	if n == 175:
		return 5
	if n == 176:
		return 5
	if n == 177:
		return 5
	if n == 178:
		return None
	if n == 179:
		return 4
	if n == 180:
		return 4
	if n == 181:
		return 5
	if n == 182:
		return 5
	if n == 183:
		return 5
	if n == 184:
		return 4
	if n == 185:
		return 5
	if n == 186:
		return 5
	if n == 187:
		return 5
	if n == 188:
		return 4
	if n == 189:
		return 4
	if n == 190:
		return 3
	if n == 191:
		return 5
	if n == 192:
		return 4
	if n == 193:
		return 5
	if n == 194:
		return 5
	if n == 195:
		return 4
	if n == 196:
		return None
	if n == 197:
		return 4
	if n == 198:
		return 4
	if n == 199:
		return 5
	if n == 200:
		return 5
	if n == 201:
		return 3
	if n == 202:
		return 5
	if n == 203:
		return 5
	if n == 204:
		return 4
	if n == 205:
		return 5
	if n == 206:
		return 5
	if n == 207:
		return 4
	if n == 208:
		return 4
	if n == 209:
		return 4
	if n == 210:
		return 4
	if n == 211:
		return None
	if n == 212:
		return 5
	if n == 213:
		return 5
	if n == 214:
		return 5
	if n == 215:
		return 5
	if n == 216:
		return 4
	if n == 217:
		return 5
	if n == 218:
		return 4
	if n == 219:
		return None
	if n == 220:
		return 5
	if n == 221:
		return None
	if n == 222:
		return 4
	if n == 223:
		return None
	if n == 224:
		return 5
	if n == 225:
		return 4
	if n == 226:
		return 5
	if n == 227:
		return None
	if n == 228:
		return 6
	if n == 229:
		return None
	if n == 230:
		return 6
	if n == 231:
		return 4
	if n == 232:
		return 6
	if n == 233:
		return None
	if n == 234:
		return 3
	if n == 235:
		return None
	if n == 236:
		return 4
	if n == 237:
		return None
	if n == 238:
		return 6
	if n == 239:
		return None
	if n == 240:
		return 6
	if n == 241:
		return None
	if n == 242:
		return 5
	if n == 243:
		return 4
	if n == 244:
		return 4
	if n == 245:
		return 3
	if n == 246:
		return 5
	if n == 247:
		return None
	if n == 248:
		return 4
	if n == 249:
		return 4
	if n == 250:
		return None
	if n == 251:
		return 5
	if n == 252:
		return 4
	if n == 253:
		return None
	if n == 254:
		return 5
	if n == 255:
		return 4
	if n == 256:
		return 4
	if n == 257:
		return 4
	if n == 258:
		return 4
	if n == 259:
		return None
	if n == 260:
		return 5
	if n == 261:
		return 4
	if n == 262:
		return 4
	if n == 263:
		return 5
	if n == 264:
		return 4
	if n == 265:
		return 4
	if n == 266:
		return 4
	if n == 267:
		return 4
	if n == 268:
		return 5
	if n == 269:
		return 4
	if n == 270:
		return 4
	if n == 271:
		return 4
	if n == 272:
		return 5
	if n == 273:
		return 4
	if n == 274:
		return None
	if n == 275:
		return 4
	if n == 276:
		return 4
	if n == 277:
		return None
	if n == 278:
		return 4
	if n == 279:
		return 4
	if n == 280:
		return 4
	if n == 281:
		return 4
	if n == 282:
		return 4
	if n == 283:
		return 5
	if n == 284:
		return None
	if n == 285:
		return 5
	if n == 286:
		return None
	if n == 287:
		return None
	if n == 288:
		return 4
	if n == 289:
		return 4
	if n == 290:
		return 5
	if n == 291:
		return 4
	if n == 292:
		return None
	if n == 293:
		return 5
	if n == 294:
		return 4
	if n == 295:
		return None
	if n == 296:
		return 5
	if n == 297:
		return 5
	if n == 298:
		return 5
	if n == 299:
		return 5
	if n == 300:
		return None
	if n == 301:
		return 5
	if n == 302:
		return None
	if n == 303:
		return 5
	if n == 304:
		return None
	if n == 305:
		return 5
	if n == 306:
		return 5
	if n == 307:
		return 4
	if n == 308:
		return 5
	if n == 309:
		return None
	if n == 310:
		return None
	if n == 311:
		return 3
	if n == 312:
		return None
	if n == 313:
		return None
	if n == 314:
		return 5
	if n == 315:
		return 5
	if n == 316:
		return 5
	if n == 317:
		return 4
	if n == 318:
		return 5
	if n == 319:
		return None
	if n == 320:
		return 5
	if n == 321:
		return 5
	if n == 322:
		return 4
	if n == 323:
		return 4
	if n == 324:
		return 3
	if n == 325:
		return None
	if n == 326:
		return 4
	if n == 327:
		return 4
	if n == 328:
		return 5
	if n == 329:
		return 4
	if n == 330:
		return 5
	if n == 331:
		return None
	if n == 332:
		return 5
	if n == 333:
		return 4
	if n == 334:
		return 6
	if n == 335:
		return 3
	if n == 336:
		return 3
	if n == 337:
		return None
	if n == 338:
		return 4
	if n == 339:
		return 4
	if n == 340:
		return 6
	if n == 341:
		return 4
	if n == 342:
		return 3
	if n == 343:
		return 5
	if n == 344:
		return 6
	if n == 345:
		return 4
	if n == 346:
		return 6
	if n == 347:
		return 4
	if n == 348:
		return 3
	if n == 349:
		return None
	if n == 350:
		return 6
	if n == 351:
		return 4
	if n == 352:
		return 4
	if n == 353:
		return 5
	if n == 354:
		return 3
	if n == 355:
		return 5
	if n == 356:
		return 5
	if n == 357:
		return 3
	if n == 358:
		return 6
	if n == 359:
		return 5
	if n == 360:
		return 4
	if n == 361:
		return 5
	if n == 362:
		return 5
	if n == 363:
		return None
	if n == 364:
		return 6
	if n == 365:
		return 4
	if n == 366:
		return 4
	if n == 367:
		return None
	if n == 368:
		return None
	if n == 369:
		return 4
	if n == 370:
		return 4
	if n == 371:
		return 5
	if n == 372:
		return None
	if n == 373:
		return 4
	if n == 374:
		return 5
	if n == 375:
		return 4
	if n == 376:
		return 5
	if n == 377:
		return None
	if n == 378:
		return 4
	if n == 379:
		return 3
	if n == 380:
		return 5
	if n == 381:
		return None
	if n == 382:
		return None
	if n == 383:
		return 4
	if n == 384:
		return 4
	if n == 385:
		return None
	if n == 386:
		return 4
	if n == 387:
		return 4
	if n == 388:
		return None
	if n == 389:
		return 2
	if n == 390:
		return None
	if n == 391:
		return None
	if n == 392:
		return None
	if n == 393:
		return 4
	if n == 394:
		return 5
	if n == 395:
		return None
	if n == 396:
		return 4
	if n == 397:
		return None
	if n == 398:
		return 4
	if n == 399:
		return None
	if n == 400:
		return None
	if n == 401:
		return None
	if n == 402:
		return 4
	if n == 403:
		return None
	if n == 404:
		return None
	if n == 405:
		return None
	if n == 406:
		return None
	if n == 407:
		return 4
	if n == 408:
		return None
	if n == 409:
		return None
	if n == 410:
		return 5
	if n == 411:
		return 4
	if n == 412:
		return 5
	if n == 413:
		return None
	if n == 414:
		return 5
	if n == 415:
		return None
	if n == 416:
		return 5
	if n == 417:
		return None
	if n == 418:
		return None
	if n == 419:
		return 5
	if n == 420:
		return 4
	if n == 421:
		return None
	if n == 422:
		return None
	if n == 423:
		return 3
	if n == 424:
		return 5
	if n == 425:
		return 4
	if n == 426:
		return 5
	if n == 427:
		return None
	if n == 428:
		return 5
	if n == 429:
		return 5
	if n == 430:
		return None
	if n == 431:
		return 4
	if n == 432:
		return 4
	if n == 433:
		return 4
	if n == 434:
		return 3
	if n == 435:
		return None
	if n == 436:
		return 5
	if n == 437:
		return 4
	if n == 438:
		return 4
	if n == 439:
		return None
	if n == 440:
		return 5
	if n == 441:
		return 4
	if n == 442:
		return 5
	if n == 443:
		return 4
	if n == 444:
		return 3
	if n == 445:
		return 4
	if n == 446:
		return 3
	if n == 447:
		return 4
	if n == 448:
		return 6
	if n == 449:
		return 4
	if n == 450:
		return 3
	if n == 451:
		return None
	if n == 452:
		return 4
	if n == 453:
		return 4
	if n == 454:
		return 6
	if n == 455:
		return 5
	if n == 456:
		return 2
	if n == 457:
		return 5
	if n == 458:
		return 5
	if n == 459:
		return 4
	if n == 460:
		return 4
	if n == 461:
		return 5
	if n == 462:
		return 3
	if n == 463:
		return 5
	if n == 464:
		return 6
	if n == 465:
		return 5
	if n == 466:
		return 6
	if n == 467:
		return None
	if n == 468:
		return 6
	if n == 469:
		return None
	if n == 470:
		return 5
	if n == 471:
		return 5
	if n == 472:
		return 5
	if n == 473:
		return 5
	if n == 474:
		return 5
	if n == 475:
		return 5
	if n == 476:
		return 5
	if n == 477:
		return 5
	if n == 478:
		return 5
	if n == 479:
		return 5
	if n == 480:
		return 5
	if n == 481:
		return 5
	if n == 482:
		return 5
	if n == 483:
		return 3
	if n == 484:
		return 5
	if n == 485:
		return None
	if n == 486:
		return 5
	if n == 487:
		return None
	if n == 488:
		return 5
	if n == 489:
		return 4
	if n == 490:
		return 5
	if n == 491:
		return 4
	if n == 492:
		return 3
	if n == 493:
		return None
	if n == 494:
		return None
	if n == 495:
		return 5
	if n == 496:
		return None
	if n == 497:
		return 3
	if n == 498:
		return 4
	if n == 499:
		return None
	if n == 500:
		return 3
	if n == 501:
		return 2
	if n == 502:
		return None
	if n == 503:
		return 4
	if n == 504:
		return 4
	if n == 505:
		return None
	if n == 506:
		return 4
	if n == 507:
		return None
	if n == 508:
		return None
	if n == 509:
		return None
	if n == 510:
		return 3
	if n == 511:
		return 4
	if n == 512:
		return None
	if n == 513:
		return 3
	if n == 514:
		return None
	if n == 515:
		return 4
	if n == 516:
		return 4
	if n == 517:
		return None
	if n == 518:
		return None
	if n == 519:
		return 5
	if n == 520:
		return None
	if n == 521:
		return 4
	if n == 522:
		return None
	if n == 523:
		return None
	if n == 524:
		return 3
	if n == 525:
		return 5
	if n == 526:
		return None
	if n == 527:
		return 5
	if n == 528:
		return 4
	if n == 529:
		return None
	if n == 530:
		return 4
	if n == 531:
		return 5
	if n == 532:
		return 5
	if n == 533:
		return 5
	if n == 534:
		return 4
	if n == 535:
		return 5
	if n == 536:
		return None
	if n == 537:
		return 5
	if n == 538:
		return 5
	if n == 539:
		return 5
	if n == 540:
		return 4
	if n == 541:
		return None
	if n == 542:
		return 3
	if n == 543:
		return 5
	if n == 544:
		return 4
	if n == 545:
		return 4
	if n == 546:
		return 4
	if n == 547:
		return 4
	if n == 548:
		return 5
	if n == 549:
		return 4
	if n == 550:
		return 5
	if n == 551:
		return None
	if n == 552:
		return 3
	if n == 553:
		return 4
	if n == 554:
		return 5
	if n == 555:
		return 4
	if n == 556:
		return 6
	if n == 557:
		return 4
	if n == 558:
		return 4
	if n == 559:
		return None
	if n == 560:
		return 3
	if n == 561:
		return 4
	if n == 562:
		return 4
	if n == 563:
		return 5
	if n == 564:
		return 6
	if n == 565:
		return None
	if n == 566:
		return 5
	if n == 567:
		return 4
	if n == 568:
		return 6
	if n == 569:
		return 4
	if n == 570:
		return 3
	if n == 571:
		return 4
	if n == 572:
		return 6
	if n == 573:
		return 4
	if n == 574:
		return 6
	if n == 575:
		return None
	if n == 576:
		return 4
	if n == 577:
		return 5
	if n == 578:
		return 2
	if n == 579:
		return 5
	if n == 580:
		return 6
	if n == 581:
		return 5
	if n == 582:
		return 6
	if n == 583:
		return 5
	if n == 584:
		return 6
	if n == 585:
		return 4
	if n == 586:
		return 5
	if n == 587:
		return 4
	if n == 588:
		return 5
	if n == 589:
		return 4
	if n == 590:
		return 6
	if n == 591:
		return None
	if n == 592:
		return None
	if n == 593:
		return None
	if n == 594:
		return 5
	if n == 595:
		return 5
	if n == 596:
		return 4
	if n == 597:
		return 3
	if n == 598:
		return None
	if n == 599:
		return 5
	if n == 600:
		return None
	if n == 601:
		return 5
	if n == 602:
		return 4
	if n == 603:
		return 4
	if n == 604:
		return 5
	if n == 605:
		return 3
	if n == 606:
		return None
	if n == 607:
		return None
	if n == 608:
		return None
	if n == 609:
		return None
	if n == 610:
		return None
	if n == 611:
		return None
	if n == 612:
		return 3
	if n == 613:
		return None
	if n == 614:
		return 4
	if n == 615:
		return None
	if n == 616:
		return None
	if n == 617:
		return 5
	if n == 618:
		return None
	if n == 619:
		return None
	if n == 620:
		return 4
	if n == 621:
		return 4
	if n == 622:
		return None
	if n == 623:
		return None
	if n == 624:
		return 5
	if n == 625:
		return 4
	if n == 626:
		return 5
	if n == 627:
		return None
	if n == 628:
		return None
	if n == 629:
		return 5
	if n == 630:
		return 4
	if n == 631:
		return None
	if n == 632:
		return None
	if n == 633:
		return 4
	if n == 634:
		return 3
	if n == 635:
		return None
	if n == 636:
		return None
	if n == 637:
		return None
	if n == 638:
		return 4
	if n == 639:
		return 4
	if n == 640:
		return None
	if n == 641:
		return None
	if n == 642:
		return 4
	if n == 643:
		return 5
	if n == 644:
		return 5
	if n == 645:
		return None
	if n == 646:
		return 5
	if n == 647:
		return 5
	if n == 648:
		return 3
	if n == 649:
		return None
	if n == 650:
		return 3
	if n == 651:
		return 4
	if n == 652:
		return 4
	if n == 653:
		return None
	if n == 654:
		return 5
	if n == 655:
		return None
	if n == 656:
		return 5
	if n == 657:
		return 4
	if n == 658:
		return 5
	if n == 659:
		return None
	if n == 660:
		return 4
	if n == 661:
		return 3
	if n == 662:
		return 5
	if n == 663:
		return None
	if n == 664:
		return 5
	if n == 665:
		return None
	if n == 666:
		return 3
	if n == 667:
		return 4
	if n == 668:
		return 3
	if n == 669:
		return 4
	if n == 670:
		return 4
	if n == 671:
		return None
	if n == 672:
		return 6
	if n == 673:
		return None
	if n == 674:
		return 5
	if n == 675:
		return 3
	if n == 676:
		return 4
	if n == 677:
		return 4
	if n == 678:
		return 6
	if n == 679:
		return 5
	if n == 680:
		return 6
	if n == 681:
		return None
	if n == 682:
		return 6
	if n == 683:
		return 5
	if n == 684:
		return 3
	if n == 685:
		return 4
	if n == 686:
		return 6
	if n == 687:
		return 4
	if n == 688:
		return 6
	if n == 689:
		return 4
	if n == 690:
		return 6
	if n == 691:
		return None
	if n == 692:
		return 4
	if n == 693:
		return 4
	if n == 694:
		return 5
	if n == 695:
		return 4
	if n == 696:
		return 6
	if n == 697:
		return 5
	if n == 698:
		return 4
	if n == 699:
		return None
	if n == 700:
		return None
	if n == 701:
		return 5
	if n == 702:
		return 3
	if n == 703:
		return 4
	if n == 704:
		return None
	if n == 705:
		return 5
	if n == 706:
		return None
	if n == 707:
		return 4
	if n == 708:
		return None
	if n == 709:
		return None
	if n == 710:
		return 4
	if n == 711:
		return 3
	if n == 712:
		return 5
	if n == 713:
		return 3
	if n == 714:
		return 5
	if n == 715:
		return 4
	if n == 716:
		return 4
	if n == 717:
		return None
	if n == 718:
		return None
	if n == 719:
		return 5
	if n == 720:
		return 4
	if n == 721:
		return None
	if n == 722:
		return None
	if n == 723:
		return 4
	if n == 724:
		return None
	if n == 725:
		return 5
	if n == 726:
		return None
	if n == 727:
		return None
	if n == 728:
		return 4
	if n == 729:
		return 4
	if n == 730:
		return None
	if n == 731:
		return 5
	if n == 732:
		return 5
	if n == 733:
		return 5
	if n == 734:
		return 5
	if n == 735:
		return 5
	if n == 736:
		return None
	if n == 737:
		return 5
	if n == 738:
		return 4
	if n == 739:
		return 5
	if n == 740:
		return 5
	if n == 741:
		return 4
	if n == 742:
		return None
	if n == 743:
		return 5
	if n == 744:
		return 4
	if n == 745:
		return None
	if n == 746:
		return 4
	if n == 747:
		return 3
	if n == 748:
		return None
	if n == 749:
		return None
	if n == 750:
		return 5
	if n == 751:
		return None
	if n == 752:
		return 4
	if n == 753:
		return 4
	if n == 754:
		return None
	if n == 755:
		return 5
	if n == 756:
		return 2
	if n == 757:
		return 5
	if n == 758:
		return None
	if n == 759:
		return 4
	if n == 760:
		return 5
	if n == 761:
		return 4
	if n == 762:
		return 4
	if n == 763:
		return None
	if n == 764:
		return 5
	if n == 765:
		return 3
	if n == 766:
		return 4
	if n == 767:
		return None
	if n == 768:
		return 4
	if n == 769:
		return 5
	if n == 770:
		return 4
	if n == 771:
		return None
	if n == 772:
		return 5
	if n == 773:
		return None
	if n == 774:
		return 4
	if n == 775:
		return 3
	if n == 776:
		return 6
	if n == 777:
		return None
	if n == 778:
		return 4
	if n == 779:
		return 3
	if n == 780:
		return 6
	if n == 781:
		return None
	if n == 782:
		return 5
	if n == 783:
		return 3
	if n == 784:
		return 6
	if n == 785:
		return 4
	if n == 786:
		return 6
	if n == 787:
		return None
	if n == 788:
		return 6
	if n == 789:
		return 5
	if n == 790:
		return 6
	if n == 791:
		return 4
	if n == 792:
		return 6
	if n == 793:
		return 4
	if n == 794:
		return 6
	if n == 795:
		return 5
	if n == 796:
		return 6
	if n == 797:
		return 5
	if n == 798:
		return 5
	if n == 799:
		return 5
	if n == 800:
		return 6
	if n == 801:
		return 4
	if n == 802:
		return 6
	if n == 803:
		return 4
	if n == 804:
		return 6
	if n == 805:
		return 5
	if n == 806:
		return 4
	if n == 807:
		return 5
	if n == 808:
		return 5
	if n == 809:
		return 4
	if n == 810:
		return 4
	if n == 811:
		return 4
	if n == 812:
		return None
	if n == 813:
		return 5
	if n == 814:
		return 4
	if n == 815:
		return 5
	if n == 816:
		return 5
	if n == 817:
		return None
	if n == 818:
		return 4
	if n == 819:
		return 4
	if n == 820:
		return 5
	if n == 821:
		return 5
	if n == 822:
		return None
	if n == 823:
		return 3
	if n == 824:
		return 4
	if n == 825:
		return 5
	if n == 826:
		return None
	if n == 827:
		return 4
	if n == 828:
		return 5
	if n == 829:
		return None
	if n == 830:
		return 5
	if n == 831:
		return None
	if n == 832:
		return None
	if n == 833:
		return 5
	if n == 834:
		return 4
	if n == 835:
		return None
	if n == 836:
		return 4
	if n == 837:
		return 3
	if n == 838:
		return None
	if n == 839:
		return None
	if n == 840:
		return 5
	if n == 841:
		return 5
	if n == 842:
		return 5
	if n == 843:
		return 4
	if n == 844:
		return None
	if n == 845:
		return 5
	if n == 846:
		return 4
	if n == 847:
		return 5
	if n == 848:
		return None
	if n == 849:
		return 4
	if n == 850:
		return 4
	if n == 851:
		return 5
	if n == 852:
		return 3
	if n == 853:
		return None
	if n == 854:
		return None
	if n == 855:
		return 3
	if n == 856:
		return 4
	if n == 857:
		return None
	if n == 858:
		return 4
	if n == 859:
		return None
	if n == 860:
		return 3
	if n == 861:
		return 3
	if n == 862:
		return None
	if n == 863:
		return None
	if n == 864:
		return 4
	if n == 865:
		return 4
	if n == 866:
		return None
	if n == 867:
		return None
	if n == 868:
		return None
	if n == 869:
		return None
	if n == 870:
		return None
	if n == 871:
		return None
	if n == 872:
		return None
	if n == 873:
		return 3
	if n == 874:
		return None
	if n == 875:
		return None
	if n == 876:
		return None
	if n == 877:
		return None
	if n == 878:
		return 4
	if n == 879:
		return None
	if n == 880:
		return None
	if n == 881:
		return None
	if n == 882:
		return 4
	if n == 883:
		return None
	if n == 884:
		return None
	if n == 885:
		return None
	if n == 886:
		return None
	if n == 887:
		return None
	if n == 888:
		return None
	if n == 889:
		return None
	if n == 890:
		return None
	if n == 891:
		return 3
	if n == 892:
		return None
	if n == 893:
		return None
	if n == 894:
		return None
	if n == 895:
		return None
	if n == 896:
		return None
	if n == 897:
		return 4
	if n == 898:
		return None
	if n == 899:
		return 4
	if n == 900:
		return None
	if n == 901:
		return None
	if n == 902:
		return None
	if n == 903:
		return None
	if n == 904:
		return None
	if n == 905:
		return 4
	if n == 906:
		return None
	if n == 907:
		return 4
	if n == 908:
		return None
	if n == 909:
		return 4
	if n == 910:
		return None
	if n == 911:
		return None
	if n == 912:
		return None
	if n == 913:
		return None
	if n == 914:
		return None
	if n == 915:
		return 4
	if n == 916:
		return None
	if n == 917:
		return 4
	if n == 918:
		return None
	if n == 919:
		return 4
	if n == 920:
		return None
	if n == 921:
		return None
	if n == 922:
		return None
	if n == 923:
		return None
	if n == 924:
		return None
	if n == 925:
		return None
	if n == 926:
		return None
	if n == 927:
		return 4
	if n == 928:
		return None
	if n == 929:
		return None
	if n == 930:
		return None
	if n == 931:
		return None
	if n == 932:
		return None
	if n == 933:
		return None
	if n == 934:
		return None
	if n == 935:
		return None
	if n == 936:
		return None
	if n == 937:
		return None
	if n == 938:
		return None
	if n == 939:
		return None
	if n == 940:
		return None
	if n == 941:
		return None
	if n == 942:
		return None
	if n == 943:
		return None
	if n == 944:
		return None
	if n == 945:
		return None
	if n == 946:
		return None
	if n == 947:
		return None
	if n == 948:
		return None
	if n == 949:
		return None
	if n == 950:
		return None
	if n == 951:
		return 3
	if n == 952:
		return None
	if n == 953:
		return None
	if n == 954:
		return None
	if n == 955:
		return None
	if n == 956:
		return None
	if n == 957:
		return None
	if n == 958:
		return None
	if n == 959:
		return None
	if n == 960:
		return None
	if n == 961:
		return None
	if n == 962:
		return None
	if n == 963:
		return 3
	if n == 964:
		return 3
	if n == 965:
		return None
	if n == 966:
		return None
	if n == 967:
		return None
	if n == 968:
		return 3
	if n == 969:
		return None
	if n == 970:
		return None
	if n == 971:
		return None
	if n == 972:
		return 3
	if n == 973:
		return None
	if n == 974:
		return None
	if n == 975:
		return None
	if n == 976:
		return None
	if n == 977:
		return None
	if n == 978:
		return None
	if n == 979:
		return None
	if n == 980:
		return None
	if n == 981:
		return None
	if n == 982:
		return None
	if n == 983:
		return None
	if n == 984:
		return None
	if n == 985:
		return None
	if n == 986:
		return None
	if n == 987:
		return None
	if n == 988:
		return None
	if n == 989:
		return None
	if n == 990:
		return None
	if n == 991:
		return None
	if n == 992:
		return None
	if n == 993:
		return None
	if n == 994:
		return None
	if n == 995:
		return None
	if n == 996:
		return None
	if n == 997:
		return None
	if n == 998:
		return None
	if n == 999:
		return None
	if n == 1000:
		return None


from collections import defaultdict
d = defaultdict(lambda : 100.0)

def parts(n, li):
	if not n:
		for b in range(2 ** (len(li) - 1)):
			bits = bin(b)[2:].zfill(len(li))
			sum_ = sum((int(k) * [1, -1][int(l)] for (k, l) in zip(li, bits)))
			d[sum_] = min(d[sum_], len(bits) - 1)
		return
	for i in range(1, len(n) + 1):
		li.append(n[:i])
		parts(n[i:], li)
		li.pop()
parts('123456789', [])

def operator_insertor(n):
	return d[n] if d[n] < 9 else None
operator_insertor(1234656)
operator_insertor(1234550)
operator_insertor(1234584)
operator_insertor(-4453)
operator_insertor(-55555)


from itertools import chain
(CACHE, INF) = ({}, float('inf'))
lst = list(chain.from_iterable((('', d) for d in '123456789')))[1:]

def dfs(i=1, nOps=0):
	if i == 17:
		v = eval(''.join(lst))
		if nOps < CACHE.get(v, INF):
			CACHE[v] = nOps
	else:
		for o in ('', '+', '-'):
			lst[i] = o
			dfs(i + 2, nOps + bool(o))
dfs()
operator_insertor = CACHE.get


from itertools import product

def operator_insertor(n):
	equation = lambda ops: ''.join((f'{a}{b}' for (a, b) in enumerate(ops + ('',), 1)))
	candidates = product(('', '+', '-'), repeat=8)
	matches = (len(''.join(ops)) for ops in candidates if eval(equation(ops)) == n)
	return min(matches, default=None)


from itertools import product

def operator_insertor(n):
	op = []
	k = []
	for y in [1, 2, 3, 4, 5, 6, 7, 8]:
		k.append([str(y)])
		k.append(['+', '-', ''])
	k.append(['9'])
	s = product(*k)
	l = []
	for e in s:
		g = ''.join(e)
		if eval(g) == n:
			l.append(len(g) - 9)
			print(g)
	return min(l) if l else None


def operator_insertor(n):
	min = 9
	for a1 in ['+', '-', '']:
		for a2 in ['+', '-', '']:
			for a3 in ['+', '-', '']:
				for a4 in ['+', '-', '']:
					for a5 in ['+', '-', '']:
						for a6 in ['+', '-', '']:
							for a7 in ['+', '-', '']:
								for a8 in ['+', '-', '']:
									expression = '1{}2{}3{}4{}5{}6{}7{}8{}9'.format(a1, a2, a3, a4, a5, a6, a7, a8)
									signs = len(expression) - 9
									if eval(expression) == n and min > signs:
										min = signs
	if min == 9:
		return None
	else:
		return min


from itertools import product, zip_longest

def operator_insertor(n):
	inserts = []
	for ops in product(('+', '-', ''), repeat=8):
		expression = ''.join(map(''.join, zip_longest('123456789', ops, fillvalue='')))
		if eval(expression) == n:
			inserts.append(len(expression) - 9)
	return min(inserts, default=None)


from itertools import chain, zip_longest

def operator_insertor(target):
	return min((x.count('+') + x.count('-') for x in insertions(target, [1, 2, 3, 4, 5, 6, 7, 8, 9])), default=None)

def insertions(rem, nums, ops=''):
	if len(nums) == 1:
		return [''.join(map(''.join, zip_longest('123456789', ops, fillvalue=''))).replace('|', '')] if rem - nums[0] == 0 else []
	return list(chain(insertions(rem - nums[0], nums[1:], ops + '+'), insertions(rem - nums[0], [-nums[1]] + nums[2:], ops + '-'), insertions(rem, [int(f'{nums[0]}{nums[1]}')] + nums[2:], ops + '|')))