PALINQUE - Palindrome Query

You've got a string s = s1s2... s|s| of length |s|, consisting of lowercase English letters. There also are q queries, each query is described by two integers li, ri (1 ≤ li ≤ ri ≤ |s|). The answer to the query is the number of substrings of string s[li... ri], which are palindromes.

String s[l... r] = slsl + 1... sr (1 ≤ l ≤ r ≤ |s|) is a substring of string s = s1s2... s|s|.

String t is called a palindrome, if it reads the same from left to right and from right to left. Formally, if t = t1t2... t|t| = t|t|t|t| - 1... t1.

Input:

The first line contains a string  s (1 ≤ |s| ≤ 5000). The second line contains a single integer q (1 ≤ q ≤ 1000000) — the number of queries. Next q lines contain the queries. The i-th of these lines contains two space-separated integers li, ri (1 ≤ li ≤ ri ≤ |s|) — the description of the i-th query.

It is guaranteed that the given string consists only of lowercase English letters.

Output:

Print q integers — the answers to the queries. Print the answers in the order, in which the queries are given in the input. Separate the printed numbers by whitespaces.

Example :


Input:

caaaba
5
1 1
1 4
2 3
4 6
4 5

 

Output:

1
7
3
4
2


Added by:Aditya Dixit
Date:2014-09-23
Time limit:10s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
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