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 MAX = 5000 + 10;
int n, q, f[MAX][MAX], check[MAX][MAX];
char s[MAX];
int main() {
  scanf("%s", &s);
  scanf("%d", &q);
  n = strlen(s);
  for (int i = n - 1; i >= 0; i--) {
    check[i][i] = 1;
    check[i][i + 1] = (s[i] == s[i + 1]);
    for (int j = i + 2; j < n; j++)
      check[i][j] = (s[i] == s[j] && check[i + 1][j - 1]);
  }
  for (int i = n - 1; i >= 0; i--) {
    f[i][i] = 1;
    f[i][i + 1] = 2 + check[i][i + 1];
    for (int j = i + 2; j < n; j++)
      f[i][j] = f[i + 1][j] + f[i][j - 1] - f[i + 1][j - 1] + check[i][j];
  }
  while (q--) {
    int i, j;
    scanf("%d %d", &i, &j);
    printf("%d\n", f[i - 1][j - 1]);
  }
}
