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;
int n;
int ans[4 * 1024 * 1024];
int lc[4 * 1024 * 1024], rc[4 * 1024 * 1024];
string str;
int lget(int a, int b) { return (a <= b) ? lc[b] - lc[a - 1] : 0; }
int rget(int a, int b) { return (a <= b) ? rc[b] - rc[a - 1] : 0; }
void build(int at, int l, int r) {
  if (l == r) {
    ans[at] = 0;
  } else {
    int mid = (l + r) / 2;
    build(at * 2, l, mid);
    build(at * 2 + 1, mid + 1, r);
    int al = ans[at * 2], ar = ans[at * 2 + 1];
    int bl = lget(l, mid), br = rget(mid + 1, r);
    bl -= al / 2, br -= ar / 2;
    ans[at] = al + ar + 2 * min(bl, br);
  }
}
int query(int at, int l, int r, int first, int second) {
  if (first > second) return 0;
  if (l == first && r == second) return ans[at];
  int mid = (l + r) / 2;
  int al = query(at * 2, l, mid, first, min(second, mid));
  int ar = query(at * 2 + 1, mid + 1, r, max(first, mid + 1), second);
  int bl = lget(first, min(second, mid));
  int br = rget(max(first, mid + 1), second);
  bl -= al / 2, br -= ar / 2;
  return al + ar + 2 * min(bl, br);
}
int a, b, q;
int main(int argc, char const* argv[]) {
  ios::sync_with_stdio(false);
  cin >> str;
  n = (int)(str.size());
  for (int i = 1; i <= n; i += 1) {
    lc[i] = lc[i - 1], rc[i] = rc[i - 1];
    if (str[i - 1] == '(')
      lc[i]++;
    else
      rc[i]++;
  }
  build(1, 1, n);
  cin >> q;
  for (int i = 0; i < q; i += 1) {
    cin >> a >> b;
    cout << query(1, 1, n, a, b) << '\n';
  }
  return 0;
}
