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 Main {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String str = in.readLine();
        int N = str.length();
        int[][] ans = new int[N][N];
        boolean[][] isPal = new boolean[N][N];
        for (int i=0; i<N; i++) {
            ans[i][i] = 1;
            isPal[i][i] = true;
            if (i>0) {
                ans[i-1][i] = ans[i-1][i-1] + ans[i][i];
                if (str.charAt(i) == str.charAt(i-1)) {
                    ans[i-1][i]++;
                    isPal[i-1][i] = true;
                }
            }
        }
        for (int size=3; size<=N; size++)
            for (int start=0; start+size-1<N; start++) {
                int end = start+size-1;
                ans[start][end] = ans[start][end-1]
                                + ans[start+1][end]
                                - ans[start+1][end-1];
                if (str.charAt(start) == str.charAt(end) && isPal[start+1][end-1]) {
                    ans[start][end]++;
                    isPal[start][end] = true;
                }
            }
        int Q = Integer.parseInt(in.readLine());
        StringBuilder sb = new StringBuilder();
        for (int q=0; q<Q; q++) {
            String[] line = in.readLine().split(" ");
            sb.append(ans[Integer.parseInt(line[0])-1][Integer.parseInt(line[1])-1] + "\n");
        }
        System.out.println(sb.toString());
    }
}