We call a number peachy if every digit in the number is either a $3$ or next to a $3.$ For example, the numbers $333,$ $83,$ $303,$ and $3773$ are all peachy, but the numbers $32523,$ $786,$ $340,$ and $3999$ are not peachy. How many positive $3$-digit numbers are peachy?
130 131 132 133 134 135 136 137 138 139 230 231 232 233 234 235 236 237 238 239 303 313 323 330 331 332 333 334 335 336 337 338 339 343 353 363 373 383 393 430 431 432 433 434 435 436 437 438 439 530 531 532 533 534 535 536 537 538 539 630 631 632 633 634 635 636 637 638 639 730 731 732 733 734 735 736 737 738 739 830 831 832 833 834 835 836 837 838 839 930 931 932 933 934 935 936 937 938 939 Total = 99 such numbers.