E. Check Transcriptiontime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputOne of Arkady's friends works at a huge radio telescope. A few decades ago the telescope has sent a signal s towards a faraway galaxy. Recently they've received a response t which they believe to be a response from aliens! The scientists now want to check if the signal t is similar to s.The original signal s was a sequence of zeros and ones (everyone knows that binary code is the universe-wide language). The returned signal t, however, does not look as easy as s, but the scientists don't give up! They represented t as a sequence of English letters and say that t is similar to s if you can replace all zeros in s with some string r_0 and all ones in s with some other string r_1 and obtain t. The strings r_0 and r_1 must be different and non-empty.Please help Arkady's friend and find the number of possible replacements for zeros and ones (the number of pairs of strings r_0 and r_1) that transform s to t.InputThe first line contains a string s (2 \le |s| \le 10^5) consisting of zeros and ones — the original signal.The second line contains a string t (1 \le |t| \le 10^6) consisting of lowercase English letters only — the received signal.It is guaranteed, that the string s contains at least one '0' and at least one '1'.OutputPrint a single integer — the number of pairs of strings r_0 and r_1 that transform s to t.In case there are no such pairs, print 0.ExamplesInput
01
aaaaaa
Output
4
Input
001
kokokokotlin
Output
2
NoteIn the first example, the possible pairs (r_0, r_1) are as follows:  "a", "aaaaa"  "aa", "aaaa"  "aaaa", "aa"  "aaaaa", "a"  The pair "aaa", "aaa" is not allowed, since r_0 and r_1 must be different.In the second example, the following pairs are possible:   "ko", "kokotlin"  "koko", "tlin" 
01
aaaaaa

4 
['brute force', 'data structures', 'hashing', 'strings', '*2100']