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 main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  string s;
  cin >> s;
  long long n = s.size();
  vector<vector<bool> > isPal(n, vector<bool>(n, false));
  vector<vector<long long> > dp(n, vector<long long>(n, 0));
  for (long long len = 1; len <= n; len++)
    for (long long start = 0; start + len - 1 < n; start++)
      if (len == 1)
        isPal[start][start + len - 1] = true;
      else
        isPal[start][start + len - 1] =
            (s[start] == s[start + len - 1]) &&
            (len == 2 ? true : isPal[start + 1][start + len - 2]);
  for (long long len = 1; len <= n; len++)
    for (long long start = 0; start + len - 1 < n; start++)
      if (len == 1)
        dp[start][start + len - 1] = 1LL;
      else
        dp[start][start + len - 1] =
            (dp[start + 1][start + len - 1] + dp[start][start + len - 2] -
             dp[start + 1][start + len - 2]) +
            (isPal[start][start + len - 1] ? 1LL : 0LL);
  long long q;
  cin >> q;
  while (q--) {
    long long x, y;
    cin >> x >> y;
    cout << dp[--x][--y] << '\n';
  }
  return 0;
}
