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 long long mxN = 4000005, mod = 1e9 + 7;
const long long INF = 1e18;
string s;
pair<long long, pair<long long, long long>> arr[mxN];
pair<long long, pair<long long, long long>> merge(
    pair<long long, pair<long long, long long>> a,
    pair<long long, pair<long long, long long>> b) {
  pair<long long, pair<long long, long long>> p;
  p.first = a.first + b.first + min(a.second.first, b.second.second);
  p.second.first =
      a.second.first - min(a.second.first, b.second.second) + b.second.first;
  p.second.second =
      a.second.second + b.second.second - min(a.second.first, b.second.second);
  return p;
}
pair<long long, pair<long long, long long>> query(long long idx, long long l,
                                                  long long r, long long si,
                                                  long long se) {
  if (si >= l && se <= r) {
    return arr[idx];
  }
  if (l > se || r < si) {
    pair<long long, pair<long long, long long>> ans;
    ans = {0, {0, 0}};
    return ans;
  }
  long long m = (si + se) / 2;
  pair<long long, pair<long long, long long>> a = query(2 * idx, l, r, si, m);
  pair<long long, pair<long long, long long>> b =
      query(2 * idx + 1, l, r, m + 1, se);
  pair<long long, pair<long long, long long>> c = merge(a, b);
  return c;
}
void build(long long l, long long r, long long idx) {
  if (l == r) {
    pair<long long, pair<long long, long long>> v = {
        0, {s[l] == '(', s[l] == ')'}};
    arr[idx] = v;
    return;
  }
  long long m = (l + r) / 2;
  build(l, m, 2 * idx);
  build(m + 1, r, 2 * idx + 1);
  arr[idx] = merge(arr[2 * idx], arr[2 * idx + 1]);
}
int32_t main() {
  cin >> s;
  long long n = s.size();
  build(0, n - 1, 1);
  long long m;
  cin >> m;
  for (long long i = 0; i < m; i++) {
    long long l, r;
    cin >> l >> r;
    pair<long long, pair<long long, long long>> ans = query(1, l, r, 1, n);
    cout << ans.first * 2 << "\n";
  }
  return 0;
}
