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 3·10^{5}.
Print to the first line the value d(s). Print sequence t_{1}, t_{2}, ..., t_{d(s)} to the following lines, where t_{i} is the number of substrings of s having diversity of exactly i.
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.