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 int n;
string s;
struct st {
  long long int size;
  long long int Op;
  long long int Cl;
  st() {
    size = 0;
    Op = 0;
    Cl = 0;
  }
};
struct st t[2000001];
struct st combine(struct st x, struct st y) {
  struct st z;
  z.size = x.size + y.size;
  long long int p = min(x.Op, y.Cl);
  z.size += p;
  x.Op -= p;
  y.Cl -= p;
  z.Op = x.Op + y.Op;
  z.Cl = x.Cl + y.Cl;
  return z;
}
void build() {
  for (long long int i = 0; i < n; i++) {
    if (s[i] == '(')
      t[n + i].Op = 1;
    else
      t[n + i].Cl = 1;
  }
  for (long long int i = n - 1; i > 0; i--) {
    t[i] = combine(t[2 * i], t[2 * i + 1]);
  }
}
void query(long long int l, long long int r) {
  l += n;
  r += n;
  struct st left, right;
  while (l < r) {
    if (l % 2 != 0) {
      left = combine(left, t[l]);
      l++;
    }
    if (r % 2 != 0) {
      --r;
      right = combine(t[r], right);
    }
    l = l / 2;
    r = r / 2;
  }
  left = combine(left, right);
  cout << 2 * left.size << "\n";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> s;
  n = s.size();
  build();
  long long int m;
  cin >> m;
  while (m--) {
    long long int l, r;
    cin >> l >> r;
    query(l - 1, r);
  }
}
