Diverse Substrings

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.

inputFormat

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.

outputFormat

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.

样例

aabacaabbad

4
                                                          14
                                                          19
                                                          28
                                                           5

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