Problem2961--Diverse Substrings

2961: Diverse Substrings

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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