Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes.

A string is 1-palindrome if and only if it reads the same backward as forward.

A string is k-palindrome (k \gt 1) if and only if:
Its left half equals to its right half. Its left and right halfs are non-empty (k-1)-palindromes.
The left half of string t is its prefix of length ⌊|t|/2⌋, and right half- the suffix of the same length. ⌊|t|/2⌋ denotes the length of string t divided by 2, rounded down.

Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times.

The first line contains the string s (1 \le |s| \le 5000) consisting of lowercase English letters.

Print |s| integers- palindromic characteristics of string s.

In the first example 1-palindromes are substring «a», «b», «b», «a», «bb», «abba», the substring «bb» is 2-palindrome. There are no 3- and 4-palindromes here.