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;
int num;
bool ok[5005][5005];
int dp[5005][5005];
int main() {
  int left, right;
  cin >> s;
  int i, j;
  int len = s.length();
  for (i = 0; i < len; i++) {
    dp[i][i] = 1;
    ok[i][i] = true, ok[i + 1][i] = true;
  }
  for (i = 2; i <= len; i++) {
    for (j = 0; j <= len - i; j++) {
      ok[j][j + i - 1] = (ok[j + 1][j + i - 2] && s[j] == s[i + j - 1]);
      dp[j][j + i - 1] = dp[j][j + i - 2] + dp[j + 1][j + i - 1] -
                         dp[j + 1][j + i - 2] + ok[j][j + i - 1];
    }
  }
  cin >> num;
  for (i = 1; i <= num; i++) {
    cin >> left >> right;
    cout << dp[left - 1][right - 1] << endl;
  }
  return 0;
}
