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;
struct info {
  int open, closed, complete;
  info() : open(0), closed(0), complete(0) {}
  info(int a, int b, int c) : open(a), closed(b), complete(c) {}
};
info combine(const info& i1, const info& i2) {
  int a = i1.open + i2.open - min(i1.open, i2.closed);
  int b = i1.closed + i2.closed - min(i1.open, i2.closed);
  int c = i1.complete + i2.complete + min(i1.open, i2.closed);
  info d = info(a, b, c);
  return d;
}
struct SegmentTree {
  int N;
  vector<info> ST;
  SegmentTree(int s, int N, string& str) : N(N) {
    ST.resize(N << 1);
    for (int i = 0; i < N; ++i)
      ST[N + i] = info(str[i] == '(', str[i] == ')', 0);
    for (int i = N - 1; i > 0; --i) ST[i] = combine(ST[i << 1], ST[i << 1 | 1]);
  }
  info query(int l, int r) {
    info resl, resr;
    for (l += N, r += N; l <= r; l >>= 1, r >>= 1) {
      if (l & 1) resl = combine(resl, ST[l++]);
      if (!(r & 1)) resr = combine(ST[r--], resr);
    }
    return combine(resl, resr);
  }
};
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  string str;
  cin >> str;
  SegmentTree st(0, str.size(), str);
  int m, l, r;
  cin >> m;
  while (m--) {
    cin >> l >> r;
    cout << (2 * st.query(l - 1, r - 1).complete) << "\n";
  }
  return 0;
}
