Canadian Computing Competition: 2000 Stage 1, Junior #2
The digits ~0~, ~1~, and ~8~ look much the same if rotated ~180~ degrees on the page (turned upside down). Also, the digit ~6~ looks much like a ~9~, and vice versa, when rotated ~180~ degrees on the page. A multi-digit number may also look like itself when rotated on the page; for example ~9966~ and ~10801~ do, but ~999~ and ~1234~ do not.
You are to write a program to count how many numbers from a given interval look like themselves when rotated ~180~ degrees on the page. For example, in the interval ~[1 \dots 100]~ there are six: ~1~, ~8~, ~11~, ~69~, ~88~, and ~96~.
Your program should take as input two integers, ~m~ and ~n~, which define the interval to be checked, ~1 \le m \le n \le 32000~. The output from your program is the number of rotatable numbers in the interval.
You may assume that all input is valid.