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 s;
bool F[5555][5555];
int G[5555][5555];
int main() {
  cin >> s;
  for (int r = 0; r < s.size(); r++)
    for (int l = r; l >= 0; l--) {
      if (l == r) F[l][r] = true;
      if (r - l == 1) F[l][r] = s[l] == s[r];
      if (r - l > 1) F[l][r] = F[l + 1][r - 1] && s[l] == s[r];
    };
  for (int r = 0; r < s.size(); r++)
    for (int l = r; l >= 0; l--)
      G[l][r] = G[l + 1][r] + G[l][r - 1] - G[l + 1][r - 1] + F[l][r];
  int q, l, r;
  scanf("%d", &q);
  for (int i = 1; i <= q; i++) {
    scanf("%d %d", &l, &r);
    --l;
    --r;
    printf("%d\n", G[l][r]);
  };
  return 0;
}
