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,...,td(s) to the following lines, where ti is the number of substrings of s having diversity of exactly i.
Examples
Input
abca
Output
3 4 3 3
Input
aabacaabbad
Output
4 14 19 28 5
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.