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 = 1e6 + 9;
string s;
struct bracket {
  int done, open, close;
};
bracket tree[3 * N];
void build(int node, int start, int end) {
  if (start == end) {
    tree[node].done = 0;
    tree[node].open = (s[start] == '(');
    tree[node].close = (s[start] == ')');
  } else {
    int mid = (start + end) / 2;
    build(2 * node, start, mid);
    build(2 * node + 1, mid + 1, end);
    int correct = min(tree[2 * node].open, tree[2 * node + 1].close);
    tree[node].done = tree[2 * node].done + tree[2 * node + 1].done + correct;
    tree[node].open = tree[2 * node].open + tree[2 * node + 1].open - correct;
    tree[node].close =
        tree[2 * node].close + tree[2 * node + 1].close - correct;
  }
}
bracket query_range(int node, int start, int end, int l, int r) {
  if (start > end or start > r or end < l) {
    bracket empty;
    empty.open = 0;
    empty.close = 0;
    empty.done = 0;
    return empty;
  }
  if (start >= l and end <= r) return tree[node];
  int mid = (start + end) / 2;
  bracket p1 = query_range(node * 2, start, mid, l, r);
  bracket p2 = query_range(node * 2 + 1, mid + 1, end, l, r);
  int correct = min(p1.open, p2.close);
  bracket p3;
  p3.done = p1.done + p2.done + correct;
  p3.open = p1.open + p2.open - correct;
  p3.close = p1.close + p2.close - correct;
  return p3;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  cin >> s;
  s = "*" + s;
  build(1, 1, s.size() - 1);
  int q, l, r;
  cin >> q;
  while (q--) {
    cin >> l >> r;
    cout << 2 * query_range(1, 1, s.size() - 1, l, r).done << '\n';
  }
  return 0;
}
