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.util.*;
import java.io.*;
public class A
{
      public static void main(String ar[]) throws Exception
      {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            char c[]=br.readLine().toCharArray();
            int n=c.length;
            boolean b[][]=new boolean[n+1][n+1];
            
            for(int d=0;d<n;d++)
            {
                  for(int i=0;i<n;i++)
                  {
                        int j=i+d;
                        if(j>=n)
                         continue;
                        if(d==0)
                         b[i+1][j+1]=true;
                        else if(d==1 && c[i]==c[j])
                         b[i+1][j+1]=true;
                        
                        if(d>=2)
                         b[i+1][j+1]=(c[i]==c[j])&&b[i+2][j];
                  }
            }
            
            int dp[][]=new int[n+1][n+1];
            for(int i=0;i<n;i++)
            {
                  for(int j=0;j<n;j++)
                   if(b[i+1][j+1])
                    dp[i+1][j+1]=1;
            }
            
            // for(int i=1;i<=n;i++)
            // {
            //       for(int j=1;j<=n;j++)
            //        System.out.print(dp[i][j]+" ");
            //       System.out.println();
            // }
            for(int i=1;i<=n;i++)
            {
                  for(int j=1;j<=n;j++)
                   dp[i][j]+=dp[i][j-1];
            }
            
            for(int j=1;j<=n;j++)
            {
                  for(int i=1;i<=n;i++)
                   dp[i][j]+=dp[i-1][j];
            }
            
            // System.out.println();
            // for(int i=0;i<=n;i++)
            // {
            //       for(int j=0;j<=n;j++)
            //        System.out.print(dp[i][j]+" ");
            //       System.out.println();
            // }
            int q=Integer.parseInt(br.readLine());
            StringBuffer sb=new StringBuffer();
            for(int i=0;i<q;i++)
            {
                  String s1[]=br.readLine().split(" ");
                  int l=Integer.parseInt(s1[0]);
                  int r=Integer.parseInt(s1[1]);
                  //System.out.println(dp[r][r]+" "+dp[l-1][l-1]+" "+dp[r][l-1]+" "+dp[l-1][r]);
                  sb.append(dp[r][r]+dp[l-1][l-1]-dp[r][l-1]-dp[l-1][r]).append("\n");
            }
            System.out.println(sb);
      }
}