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 l, r;
const int MAXN = 1e6 * 4;
int open[MAXN], close[MAXN], valid[MAXN];
string s;
inline void operate(int root) {
  int mi = min(open[root << 1], close[root << 1 | 1]);
  valid[root] = mi * 2 + valid[root << 1] + valid[root << 1 | 1];
  open[root] = open[root << 1] + open[root << 1 | 1] - mi;
  close[root] = close[root << 1] + close[root << 1 | 1] - mi;
}
void build(int root, int le, int re) {
  if (le == re) {
    if (s[le] == '(')
      open[root]++;
    else
      close[root]++;
    return;
  }
  int mid = (le + re) / 2;
  build(root << 1, le, mid);
  build(root << 1 | 1, mid + 1, re);
  operate(root);
}
int getOpen(tuple<int, int, int> &x) { return get<1>(x); }
int getClose(tuple<int, int, int> &x) { return get<2>(x); }
int getValid(tuple<int, int, int> &x) { return get<0>(x); }
tuple<int, int, int> query(int root, int beg, int end) {
  if (end < l || beg > r) {
    return make_tuple(0, 0, 0);
  }
  if (l <= beg && r >= end) {
    return make_tuple(valid[root], open[root], close[root]);
  }
  int mid = (beg + end) / 2;
  tuple<int, int, int> r1 = query(root << 1, beg, mid);
  tuple<int, int, int> r2 = query(root << 1 | 1, mid + 1, end);
  int mi = min(getOpen(r1), getClose(r2));
  return make_tuple(getValid(r1) + getValid(r2) + 2 * mi,
                    getOpen(r1) + getOpen(r2) - mi,
                    getClose(r1) + getClose(r2) - mi);
}
int main() {
  int q;
  while (cin >> s) {
    int len = s.size();
    build(1, 0, len - 1);
    cin >> q;
    while (q--) {
      cin >> l >> r;
      l--;
      r--;
      tuple<int, int, int> res = query(1, 0, len - 1);
      cout << getValid(res) << endl;
    }
  }
  return 0;
}
