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;
long long MAXN = 1000001;
struct data {
  long long el, er, ans;
} t[4000004];
data combine(data l, data r) {
  data res;
  res.ans = l.ans + r.ans + min(l.el, r.er);
  res.el = l.el + r.el - min(l.el, r.er);
  res.er = l.er + r.er - min(l.el, r.er);
  return res;
}
data make_data(long long val) {
  data res;
  if (val == 1) {
    res.el = 1;
    res.er = 0;
  } else if (val == 2) {
    res.er = 1;
    res.el = 0;
  } else {
    res.er = 0;
    res.el = 0;
  }
  res.ans = 0;
  return res;
}
void build(long long a[], long long v, long long tl, long long tr) {
  if (tl == tr) {
    t[v] = make_data(a[tl]);
  } else {
    long long tm = (tl + tr) / 2;
    build(a, v * 2, tl, tm);
    build(a, v * 2 + 1, tm + 1, tr);
    t[v] = combine(t[v * 2], t[v * 2 + 1]);
  }
}
data query(long long v, long long tl, long long tr, long long l, long long r) {
  if (l > r) return make_data(0);
  if (tl == l && tr == r) {
    return t[v];
  }
  long long tm = (tl + tr) / 2;
  return combine(query(v * 2, tl, tm, l, min(r, tm)),
                 query(v * 2 + 1, tm + 1, tr, max(l, tm + 1), r));
}
int main() {
  ios::sync_with_stdio(0);
  string str;
  cin >> str;
  long long n = str.length();
  long long a[n];
  for (long long i = 0; i < n; i++) {
    if (str[i] == '(')
      a[i] = 1;
    else
      a[i] = 2;
  }
  build(a, 1, 0, n - 1);
  long long m;
  cin >> m;
  while (m--) {
    long long l, r;
    cin >> l >> r;
    l--;
    r--;
    cout << 2 * query(1, 0, n - 1, l, r).ans << endl;
  }
  return 0;
}
