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>
char str[5005];
int fun(int a, int b);
int m[5005][5005];
bool isP(int a, int b);
int es[5005][5005];
bool judge(int a, int b);
int main() {
  memset(str, 0, sizeof(str));
  memset(m, 0, sizeof(m));
  memset(es, -1, sizeof(es));
  for (int i = 0; i <= 5000; i++) es[i][i] = 1;
  gets(str);
  int K;
  scanf("%d", &K);
  for (int k = 0; k < K; k++) {
    int a, b, ans = 0;
    scanf("%d %d", &a, &b);
    ans = fun(a - 1, b - 1);
    printf("%d\n", ans);
  }
  return 0;
}
int fun(int a, int b) {
  if (m[a][b] != 0) return m[a][b];
  if (a == b) return 1;
  if (a > b) return 0;
  if (isP(a, b) == true) {
    m[a + 1][b] = fun(a + 1, b);
    m[a][b - 1] = fun(a, b - 1);
    m[a + 1][b - 1] = fun(a + 1, b - 1);
    return m[a][b] = m[a + 1][b] + m[a][b - 1] - m[a + 1][b - 1] + 1;
  } else {
    m[a + 1][b] = fun(a + 1, b);
    m[a][b - 1] = fun(a, b - 1);
    m[a + 1][b - 1] = fun(a + 1, b - 1);
    return m[a][b] = m[a + 1][b] + m[a][b - 1] - m[a + 1][b - 1];
  }
}
bool isP(int a, int b) {
  if ((a + 1) == b) {
    if (str[a] != str[b])
      return false;
    else
      return true;
  }
  if (es[a][b] != -1) {
    if (es[a][b] == 0)
      return false;
    else
      return true;
  } else {
    if (es[a + 1][b - 1] != -1) {
      es[a][b] = es[a + 1][b - 1] == 1 && str[a] == str[b];
      if (es[a][b] == 1)
        return true;
      else
        return false;
    } else {
      es[a + 1][b - 1] = judge(a + 1, b - 1);
      es[a][b] = es[a + 1][b - 1] == 1 && str[a] == str[b];
      if (es[a][b] == 1)
        return true;
      else
        return false;
    }
  }
}
bool judge(int a, int b) {
  int flag = 1;
  int i, j;
  for (i = a, j = b; i < j; i++, j--)
    if (str[i] != str[j]) {
      flag = 0;
      break;
    }
  if (flag == 1)
    return true;
  else
    return false;
}
