CF835D · Palindromic characteristics

• 难度：1900
• 标签：brute force、dp、hashing、strings
• 链接：https://codeforces.com/problemset/problem/835/D
• 时间限制：3 seconds　内存限制：256 megabytes
• 出现位置：Day29-阶段模拟8-高压综合卷

英文原题面

Statement

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:

• 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.

Input

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

Output

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

样例

样例 1

输入：

abba

输出：

6 1 0 0 

样例 2

输入：

abacaba

输出：

12 4 1 0 0 0 0 

样例解释（英文原文）

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.