Sereja has a bracket sequence s1, s2, ..., sn, or, in other words, a string s of length n, consisting of characters "(" and ")".

Sereja needs to answer m queries, each of them is described by two integers li, ri (1 ≤ li ≤ ri ≤ n). The answer to the i-th query is the length of the maximum correct bracket subsequence of sequence sli, sli + 1, ..., sri. Help Sereja answer all queries.

You can find the definitions for a subsequence and a correct bracket sequence in the notes.

Input

The first line contains a sequence of characters s1, s2, ..., sn (1 ≤ n ≤ 106) without any spaces. Each character is either a "(" or a ")". The second line contains integer m (1 ≤ m ≤ 105) — the number of queries. Each of the next m lines contains a pair of integers. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n) — the description of the i-th query.

Output

Print the answer to each question on a single line. Print the answers in the order they go in the input.

Examples

Input

())(())(())(
7
1 1
2 3
1 2
1 12
8 12
5 11
2 10


Output

0
0
2
10
4
6
6

Note

A subsequence of length |x| of string s = s1s2... s|s| (where |s| is the length of string s) is string x = sk1sk2... sk|x| (1 ≤ k1 < k2 < ... < k|x| ≤ |s|).

A correct bracket sequence is a bracket sequence that can be transformed into a correct aryphmetic expression by inserting characters "1" and "+" between the characters of the string. For example, bracket sequences "()()", "(())" are correct (the resulting expressions "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.

For the third query required sequence will be «()».

For the fourth query required sequence will be «()(())(())».
#include <bits/stdc++.h>
using namespace std;
const double eps(1e-8);
char s[1000010];
int n, m, a, b;
vector<int> vec[1000010];
vector<int> p[1000010];
int x[1000010], y[1000010], sum[1000010], ans[1000010];
int Lowbit(int x) { return x & (-x); }
void Update(int pos, int val) {
  while (pos > 0) {
    sum[pos] += val;
    pos -= Lowbit(pos);
  }
}
int Query(int pos) {
  int ret = 0;
  while (pos <= n) {
    ret += sum[pos];
    pos += Lowbit(pos);
  }
  return ret;
}
void Add(int l, int r, int val) {
  Update(r, val);
  Update(l - 1, -val);
}
int main() {
  scanf("%s", s + 1);
  for (n = 1; s[n]; n++)
    ;
  n--;
  scanf("%d", &m);
  for (int i = 1; i <= m; i++) {
    scanf("%d%d", &a, &b);
    vec[b].push_back(a);
    p[b].push_back(i);
  }
  int len = 0;
  for (int i = 1; i <= n; i++) {
    len++;
    if (s[i] == '(')
      x[len] = 0;
    else
      x[len] = 1;
    y[len] = i;
    if (len >= 2 && x[len] == 1 && x[len - 1] == 0) {
      Add(1, y[len - 1], 2);
      len -= 2;
    }
    for (int j = 0; j < (int)vec[i].size(); j++) {
      int tmp = vec[i][j];
      ans[p[i][j]] = Query(tmp);
    }
  }
  for (int i = 1; i <= m; i++) printf("%d\n", ans[i]);
  return 0;
}
