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 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.

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.

Examples

Input

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


Output

1
7
3
4
2

Note

Consider the fourth query in the first test case. String s[4... 6] = «aba». Its palindrome substrings are: «a», «b», «a», «aba».
import java.io.*;
import java.util.*;

public class Codeforces
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        char c[]=bu.readLine().toCharArray();
        int n=c.length,i,j,dp[][]=new int[n][n];
        boolean p[][]=new boolean[n][n];
        for(i=0;i<n;i++) p[i][i]=true;

        for(i=2;i<=n;i++)
        for(j=0;j+i<=n;j++)
        {
            int r=j+i-1;
            if(i==2) p[j][r]=(c[j]==c[r]);
            else p[j][r]=p[j+1][r-1]&(c[j]==c[r]);
        }

        int add[]=new int[n];
        for(i=n-1;i>=0;i--)
        for(j=i;j<n;j++)
        {
            if(p[i][j]) add[j]++;
            dp[i][j]=add[j];
            if(j>i) dp[i][j]+=dp[i][j-1];
        }

        int q=Integer.parseInt(bu.readLine());
        while(q-->0)
        {
            String s[]=bu.readLine().split(" ");
            int l=Integer.parseInt(s[0]),r=Integer.parseInt(s[1]);
            sb.append(dp[l-1][r-1]+"\n");
        }
        System.out.print(sb);
    }
}