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.
The first line contains string s (1≤|s|≤5000). The second line contains a single integer q (1≤q≤106) − 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.
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.
caaaba
5
1 1
1 4
2 3
4 6
4 5
1
7
3
4
2
Consider the fourth query in the first test case. String s[4... 6] = «aba». Its palindrome substrings are: «a», «b», «a», «aba».