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 int N = 1000006;
char s[N];
pair<int, int> st[4 * N];
pair<int, int> process(const pair<int, int> &x, const pair<int, int> &y) {
  int matched = min(x.second, y.first);
  return {y.first - matched + x.first, x.second - matched + y.second};
}
void build(int l, int r, int i = 1) {
  if (l == r) {
    st[i] = {s[l] == ')', s[l] == '('};
    return;
  }
  int mid = (l + r) >> 1, li = i << 1, ri = li + 1;
  build(l, mid, li);
  build(mid + 1, r, ri);
  st[i] = process(st[li], st[ri]);
}
pair<int, int> query(int l, int r, int x, int y, int i = 1) {
  if (r < x || l > y) {
    return {0, 0};
  }
  if (x <= l && r <= y) {
    return st[i];
  }
  int mid = (l + r) >> 1, li = i << 1, ri = li + 1;
  auto ql = query(l, mid, x, y, li);
  auto qr = query(mid + 1, r, x, y, ri);
  return process(ql, qr);
}
int main() {
  int m;
  scanf("%s %d", s, &m);
  int n = strlen(s);
  build(0, n - 1);
  while (m--) {
    int l, r;
    scanf("%d %d", &l, &r);
    auto res = query(0, n - 1, l - 1, r - 1);
    printf("%d\n", r - l + 1 - res.first - res.second);
  }
}
