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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Solution {
    private static int MAX = Integer.MAX_VALUE;
    private static int[] lengths;
    private static int[][] lists;
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        char[] arr = reader.readLine().toCharArray();
        int n = arr.length;
        lengths = new int[n];
        lists = new int[n][n];
        for (int i=0; i<n; i++) Arrays.fill(lists[i], MAX);
        //iterate over palindroms with odd length;
        for (int i=0; i<n; i++) {
            int j1 = i, j2=i;
            while (j1>-1 && j2<n) {
                if (arr[j1]!=arr[j2]) break;
                lists[j1][lengths[j1]] = j2;
                lengths[j1]++;
                j1--; j2++;
            }
        }
        //iterate over palindroms with even length;
        for (int i=0; i<n; i++) {
            int j1 = i, j2 = i+1;
            while (j1>-1 && j2<n) {
                if (arr[j1]!=arr[j2]) break;
                lists[j1][lengths[j1]] = j2;
                lengths[j1]++;
                j1--; j2++;
            }
        }
        //sort lists;
        for (int i=0; i<n; i++) Arrays.sort(lists[i]);
        //making matrix of results;
        int[][] res = new int[n][n];
        for (int l=n-1; l>-1; l--) {
            int j = -1;
            int maxj = lengths[l] - 1;
            for (int r=0; r<n; r++) {
                while (j<maxj && lists[l][j+1]<=r) {
                    j++;
                }
                res[l][r] = j+1;
                if (l<n-1) res[l][r]+=res[l+1][r];
            }
        }
        //answering the queries;
        int t = Integer.parseInt(reader.readLine());
        StringBuilder ans = new StringBuilder();
        while (t-->0) {
            StringTokenizer sToken = new StringTokenizer(reader.readLine());
            int l = Integer.parseInt(sToken.nextToken()) - 1;
            int r = Integer.parseInt(sToken.nextToken()) - 1;
            ans.append(res[l][r]).append("\n");
        }
        System.out.println(ans);
    }
}