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;
string s;
pair<int, int> st[3000002];
void build(int v, int l, int r) {
  if (l == r) {
    st[v] = make_pair(s[l] == '(', s[l] == ')');
    return;
  }
  int lv, rv, mid;
  lv = 2 * v;
  rv = 2 * v + 1;
  mid = (l + r) / 2;
  build(lv, l, mid);
  build(rv, mid + 1, r);
  st[v].first = st[rv].first + max(0, st[lv].first - st[rv].second);
  st[v].second = st[lv].second + max(0, st[rv].second - st[lv].first);
}
pair<int, int> query(int v, int l, int r, int L, int R) {
  if (r < L || R < l) return make_pair(0, 0);
  if (L <= l && r <= R) return st[v];
  pair<int, int> L1 = query(2 * v, l, (l + r) / 2, L, R);
  pair<int, int> R1 = query(2 * v + 1, (l + r) / 2 + 1, r, L, R);
  return make_pair(R1.first + max(0, L1.first - R1.second),
                   L1.second + max(0, R1.second - L1.first));
}
int main() {
  cin >> s;
  int n = s.length();
  build(1, 0, n - 1);
  int m;
  cin >> m;
  for (int i = 0; i < m; ++i) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    pair<int, int> q = query(1, 0, n - 1, l, r);
    cout << r - l + 1 - (q.first + q.second) << "\n";
  }
  return 0;
}
