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».
#include <bits/stdc++.h>
using namespace std;
string str;
int q, l, r, dp[5050][5050];
bool ispali[5050][5050];
int main() {
  cin >> str >> q;
  int n = str.size();
  for (int k = 0; k < n; k++) {
    if (k && str[k] == str[k - 1]) {
      ispali[k - 1][k] = 1;
      dp[k - 1][k] = 3;
    } else if (k)
      dp[k - 1][k] = 2;
    ispali[k][k] = 1;
    dp[k][k] = 1;
  }
  for (int k = 2; k < n; k++)
    for (int i = 0; i + k < n; i++) {
      if (str[i] == str[i + k] && ispali[i + 1][i + k - 1])
        ispali[i][i + k] = 1;
      dp[i][i + k] = dp[i + 1][i + k] + dp[i][i + k - 1] -
                     dp[i + 1][i + k - 1] + ispali[i][i + k];
    }
  while (q--) {
    scanf("%d %d", &l, &r);
    printf("%d\n", dp[--l][--r]);
  }
  return 0;
}
