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.awt.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;

public class Main {
    static int mod = (int) 1e9 + 7;
    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();
        String s=sc.nextLine();
        int n=s.length();
        s=" "+s;
        int[][] dp=new int[n+1][n+1];

        for(int i=1;i<=n;i++)dp[i][i]=1;
        for(int i=1;i<n;i++){
            if(s.charAt(i)==s.charAt(i+1))dp[i][i+1]=1;
        }
        for(int len=0;len<n-2;len++){
            for(int i=1;i<n-len;i++){
                if(dp[i][i+len]==1 && s.charAt(i-1)==s.charAt(i+len+1)){
                    dp[i-1][i+len+1]=1;
                }
            }
        }
        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];
        }

        StringBuilder sb=new StringBuilder();
        int q=sc.nextInt();
        while(q-->0){
            int a=sc.nextInt(),b=sc.nextInt();
            sb.append(dp[b][b]-dp[b][a-1]-dp[a-1][b]+dp[a-1][a-1]+"\n");
        }
        System.out.println(sb);
    }
}

class FastReader {
    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}