URAL1960-Palindromes and Super Abilities

Palindromes and Super Abilities

Time limit: 1.0 second
Memory limit: 64 MB

After solving seven problems on Timus Online Judge with a word “palindrome” in the problem name, Misha has got an unusual ability. Now, when he reads a word, he can mentally count the number of unique nonempty substrings of this word that are palindromes.

Dima wants to test Misha’s new ability. He adds letters  s 1, ...,  s n to a word, letter by letter, and after every letter asks Misha, how many different nonempty palindromes current word contains as substrings. Which  n numbers will Misha say, if he will never be wrong?

Input

The only line of input contains the string  s 1... s n, where  s i are small English letters (1 ≤  n ≤ 10 5).

Output

Output  n numbers separated by whitespaces,  i-th of these numbers must be the number of different nonempty substrings of prefix  s 1... s i that are palindromes.

Sample

input	output
aba	1 2 3

Problem Author: Mikhail Rubinchik (prepared by Grigory Nazarov)
Problem Source: Ural FU contest. Kontur Cup. Petrozavodsk training camp. Winter 2013

题意：给你一个字符串，求出每个前缀有多少种回文串

解题思路：回文树，回文树每开一个新节点就是一种新的回文串

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