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 node {
  int open;
  int close;
  int balanced;
};
void build(int i, int w, vector<node> &seg_tree) {
  if (i >= w) {
    return;
  }
  build(2 * i, w, seg_tree);
  build(2 * i + 1, w, seg_tree);
  node left = seg_tree[2 * i];
  node right = seg_tree[2 * i + 1];
  seg_tree[i].balanced =
      left.balanced + right.balanced + min(left.open, right.close);
  seg_tree[i].open = right.open + max(left.open - right.close, 0);
  seg_tree[i].close = left.close + max(right.close - left.open, 0);
}
node query(int i, int ql, int qr, int l, int r, vector<node> &seg_tree) {
  if (ql == l && qr == r) {
    return seg_tree[i];
  }
  int mid = (l + r) / 2;
  if (qr <= mid) {
    return query(2 * i, ql, qr, l, mid, seg_tree);
  }
  if (ql >= mid) {
    return query(2 * i + 1, ql, qr, mid, r, seg_tree);
  }
  node left = query(2 * i, ql, mid, l, mid, seg_tree);
  node right = query(2 * i + 1, mid, qr, mid, r, seg_tree);
  node ret_node;
  ret_node.balanced =
      left.balanced + right.balanced + min(left.open, right.close);
  ret_node.open = right.open + max(left.open - right.close, 0);
  ret_node.close = left.close + max(right.close - left.open, 0);
  return ret_node;
}
int main() {
  string s;
  cin >> s;
  int n = s.length();
  int temp = n, count = 0, w;
  while (temp != 0) {
    temp /= 2;
    count++;
  }
  w = 1 << count;
  vector<node> seg_tree(2 * w);
  for (int i = w; i < w + n; ++i) {
    seg_tree[i].open = 0;
    seg_tree[i].close = 0;
    seg_tree[i].balanced = 0;
    if (s[i - w] == '(') {
      seg_tree[i].open++;
    } else {
      seg_tree[i].close++;
    }
  }
  build(1, w, seg_tree);
  int l, r, m;
  cin >> m;
  while (m--) {
    cin >> l >> r;
    cout << 2 * query(1, l - 1, r, 0, w, seg_tree).balanced << '\n';
  }
}
