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.

Input

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.

Output

Print to the first line the value d(s). Print sequence t₁, t₂, ..., t_d(s) to the following lines, where t_i is the number of substrings of s having diversity of exactly i.

Note

Consider the first example.

We denote by s(i, j) a substring of "abca" with the indices in the segment [i, j].

s(1, 1) = "a", d("a") = 1
s(2, 2) = "b", d("b") = 1
s(3, 3) = "c", d("c") = 1
s(4, 4) = "a", d("a") = 1
s(1, 2) = "ab", d("ab") = 2
s(2, 3) = "bc", d("bc") = 2
s(3, 4) = "ca", d("ca") = 2
s(1, 3) = "abc", d("abc") = 3
s(2, 4) = "bca", d("bca") = 3
s(1, 4) = "abca", d("abca") = 3

Total number of substring with diversity 1 is 4, with diversity 2 equals 3, 3 diversity is 3.

Diverse Substrings

Examples