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;
const int N = 5005;
char s[N];
int n, dp[N][N];
int main() {
  scanf("%s", s + 1);
  n = strlen(s + 1);
  for (int l = n; l; --l) {
    for (int r = l; r <= n; ++r) {
      dp[l][r] = (l + 1 >= r || dp[l + 1][r - 1]) && s[l] == s[r];
    }
  }
  for (int l = n; l; --l) {
    for (int r = l; r <= n; ++r) {
      dp[l][r] += dp[l + 1][r] + dp[l][r - 1] - dp[l + 1][r - 1];
    }
  }
  int q, l, r;
  scanf("%d", &q);
  while (q--) {
    scanf("%d%d", &l, &r);
    printf("%d\n", dp[l][r]);
  }
}
