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.StringTokenizer;

public class appl {
    static BufferedReader br = new BufferedReader(new InputStreamReader(
            System.in));
    static StringTokenizer tok;

    private static String nextToken() {
        while (tok == null || !tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }
        return tok.nextToken();
    }

    private static int nextInt() {
        return Integer.parseInt(nextToken());
    }

    public static void main(String[] args) {
        byte[][] array = new byte[5000][5000];
        int[][] pals = new int[5000][5000];
        String str = nextToken();
        int strlen = str.length();

        for (int i = 0; i < strlen; i++) {
            array[i][i] = 1;
            pals[i][i] = 1;
        }

        for (int i = 1; i < strlen; i++) {
            for (int j = i - 1; j >= 0; j--) {
                if (i - j > 1 && array[i - 1][j + 1] == 1
                        && str.charAt(i) == str.charAt(j)) {
                    array[i][j] = 1;

                } else if (i - j <= 1 && str.charAt(i) == str.charAt(j)) {
                    array[i][j] = 1;
                    pals[i][j] = 3;
                } else if (i - j <= 1 && str.charAt(i) != str.charAt(j)) {
                    pals[i][j] = 2;
                }
                if(i - j > 1){
                    pals[i][j] = pals[i - 1][j] + pals[i][j + 1]
                            - pals[i - 1][j + 1] + array[i][j];

                }

                // pals[i][j] = pals[i - 1][j] + 1;
                // for (int k = j; k < i; k++) {
                // pals[i][j] += array[i][k];
                // }

            }
        }

         int count = nextInt();
         for (int i = 0; i < count; i++) {
         int l = nextInt(), r = nextInt();
         System.out.println(pals[r - 1][l - 1]);
         }

//      for (int i = 0; i < str.length(); i++) {
//          for (int j = 0; j < str.length(); j++) {
//              System.out.print(pals[i][j]);
//              System.out.print(" ");
//          }
//          System.out.println();
//      }

    }

}
