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.*;
import java.awt.Point;
import static java.lang.Math.*;

public class P245H {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        char[] S = in.readLine().toCharArray();
        int n = S.length;
        boolean[][] pal = new boolean[n][n];
        for(int len=0; len<n; len++)
            for(int st=0; st+len<n; st++) {
                if(len == 0) pal[st][st+len] = true;
                else if(len == 1) pal[st][st+len] = S[st]==S[st+len];
                else pal[st][st+len] = S[st]==S[st+len] && pal[st+1][st+len-1];
            }
        int[][] dp = new int[n][n];
        for(int len=0; len<n; len++) {
            for(int st=0; st+len<n; st++) {
                if(len == 0) dp[st][st+len] = 1;
                else if(len == 1) dp[st][st+len] = 2 + (pal[st][st+len]?1:0);
                else {
                    dp[st][st+len] = dp[st+1][st+len]+dp[st][st+len-1]
                        -dp[st+1][st+len-1] + (pal[st][st+len]?1:0);
                }
            }
        }

        StringBuilder out = new StringBuilder();
        int q = i(in.readLine());
        for(int i=0; i<q; i++) {
            String[] arr = in.readLine().split(" ");
            int x = i(arr[0])-1;
            int y = i(arr[1])-1;
            out.append(dp[x][y]+"\n");
        }
        System.out.print(out);
    }

    public static <T> List<T> list() { return new ArrayList<T>(); }
    public static <K,V> Map<K,V> map() { return new HashMap<K,V>(); }
    public static int i(String s) { return Integer.parseInt(s); }
    public static long l(String s) { return Long.parseLong(s); }
}
