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 dp[5002][5002];
int len;
string str;
void dpfun(int, int);
void init();
int main() {
  int n, a, b;
  cin >> str >> n;
  init();
  for (int i = 1; i <= n; i++) {
    scanf("%d%d", &a, &b);
    printf("%d\n", dp[a - 1][b - 1]);
  }
}
void init() {
  len = str.length();
  for (int i = 0; i < len; i++) {
    dpfun(i, i);
    if (i + 1 < len) dpfun(i, i + 1);
  }
  for (int i = 0; i < len; i++) {
    for (int j = i + 1; j < len; j++) {
      dp[i][j] += dp[i][j - 1];
    }
  }
  for (int i = len - 1; i >= 0; i--) {
    for (int j = i + 1; j < len; j++) {
      dp[i][j] += dp[i + 1][j];
    }
  }
}
void dpfun(int i, int j) {
  while (i >= 0 && j < len && str[i] == str[j]) {
    dp[i--][j++]++;
  }
}
