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;
long long int v[5005][5005];
int main() {
  long long int i, j, n, q, a, b, c = 0, k = 0;
  ios_base::sync_with_stdio(false);
  string s;
  cin >> s >> q;
  n = s.size();
  for (i = 1; i <= n; i++) v[i][i] = 1;
  for (i = 1; i < n; i++) {
    if (s[i - 1] == s[i]) v[i][i + 1] = 1;
  }
  for (j = 2; j < n; j++) {
    for (i = 1; i <= n; i++) {
      if (i + j > n) break;
      if (v[i + 1][i + j - 1] && s[i - 1] == s[i + j - 1]) v[i][i + j] = 1;
    }
  }
  for (i = 1; i <= n; i++) {
    for (j = 1; j <= n; j++)
      v[i][j] += v[i - 1][j] + v[i][j - 1] - v[i - 1][j - 1];
  }
  while (q--) {
    cin >> a >> b;
    printf("%lld\n", v[b][b] - v[b][a - 1] - v[a - 1][b] + v[a - 1][a - 1]);
  }
}
