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 > 1) if and only if: 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 ≤ |s| ≤ 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.