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;
int n, a[10005], b[10005], d[5002][5002], i, j, q, l, r;
char s[10005];
void Init() {
  cin >> s;
  n = strlen(s);
  for (i = 0; i < n; i++) {
    while (i - a[i] >= 0 && i + a[i] < n && s[i - a[i]] == s[i + a[i]]) {
      d[i - a[i]][i + a[i]]++;
      a[i]++;
    }
    while (i - b[i] - 1 >= 0 && i + b[i] < n &&
           s[i - b[i] - 1] == s[i + b[i]]) {
      d[i - b[i] - 1][i + b[i]]++;
      b[i]++;
    }
  }
  for (i = n - 1; i >= 0; i--) {
    for (j = i; j <= n; j++) {
      d[i][j] += d[i + 1][j] + d[i][j - 1] - d[i + 1][j - 1];
    }
  }
  cin >> q;
  for (i = 0; i < q; i++) {
    cin >> l >> r;
    printf("%d\n", d[l - 1][r - 1]);
  }
}
void solve() {}
int main() {
  Init();
  solve();
  return 0;
}
