String diversity is the number of symbols that occur in the string at least once. Diversity of s will be denoted by d(s). For example , d("aaa")=1, d("abacaba")=3.
Given a string s, consisting of lowercase Latin letters. Consider all its substrings. Obviously, any substring diversity is a number from 1 to d(s). Find statistics about substrings diversity: for each k from 1 to d(s), find how many substrings of s has a diversity of exactly k.
The input consists of a single line containing s. It contains only lowercase Latin letters, the length of s is from 1 to 3·105.
Print to the first line the value d(s). Print sequence t1,t2,...,td(s) to the following lines, where ti is the number of substrings of s having diversity of exactly i.
abca
3
4
3
3
aabacaabbad
4
14
19
28
5
Consider the first example.
We denote by s(i,j) a substring of "abca" with the indices in the segment [i,j].
Total number of substring with diversity 1 is 4, with diversity 2 equals 3, 3 diversity is 3.