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.*;
import java.util.*;

public class queriesPalindromes {
  public static void main(String[] args) throws Exception {
    BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
    BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));
    String s = r.readLine();
    int n = s.length();
    int numQueries = Integer.parseInt(r.readLine());
    int[][] storage = new int[5005][5005];
    boolean[][] pal = new boolean[5005][5005];
    for (int i = 0; i < n; i++) {
      pal[i][i] = true;
      pal[i + 1][i] = true;
      storage[i][i] = 1;
    }
    for (int i = 2; i < n + 1; i++) {
      for (int k = 0; k < n - i + 1; k++) {
        pal[k][k + i - 1] = (s.charAt(k) == s.charAt(k + i - 1)) && pal[k + 1][k + i - 2];
        int num = pal[k][k + i - 1] ? 1 : 0;
        storage[k][k + i - 1] = storage[k][k + i - 2] + storage[k + 1][k + i - 1]
                                + num - storage[k + 1][k + i - 2] ;
      }
    } 
    for (int i = 0; i < numQueries; i++) {
      StringTokenizer st = new StringTokenizer(r.readLine());
      int a = Integer.parseInt(st.nextToken());
      int b = Integer.parseInt(st.nextToken());
      w.write("" + storage[a - 1][b - 1] + "\n");
    }
   w.close();
   System.exit(0);
  }
}
