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;
struct segtree {
  long long siz;
  pair<long long, long long> NEUTRAL_ELEMENT = make_pair(0, 0);
  vector<pair<long long, long long> > node;
  pair<long long, long long> marge(pair<long long, long long> a,
                                   pair<long long, long long> b) {
    long long mn = min(a.second, b.first);
    a.second -= mn;
    b.first -= mn;
    return make_pair(a.first + b.first, a.second + b.second);
  }
  pair<long long, long long> single(char a) {
    if (a == '(')
      return make_pair(0, 1);
    else
      return make_pair(1, 0);
  }
  segtree(string &A) {
    long long n = A.size();
    siz = 1;
    while (siz < n) siz *= 2;
    node.assign(2 * siz, NEUTRAL_ELEMENT);
    build(A, 1, 1, siz);
  }
  void build(string &A, long long x, long long lx, long long rx) {
    if (lx == rx) {
      if (lx <= A.size()) {
        node[x] = single(A[lx - 1]);
      }
      return;
    }
    long long m = (lx + rx) / 2;
    build(A, 2 * x, lx, m);
    build(A, 2 * x + 1, m + 1, rx);
    node[x] = marge(node[2 * x], node[2 * x + 1]);
  }
  pair<long long, long long> query(long long l, long long r, long long x,
                                   long long lx, long long rx) {
    if (lx > r || l > rx) return NEUTRAL_ELEMENT;
    if (lx >= l && rx <= r) return node[x];
    long long m = (lx + rx) / 2;
    pair<long long, long long> s1 = query(l, r, 2 * x, lx, m);
    pair<long long, long long> s2 = query(l, r, 2 * x + 1, m + 1, rx);
    return marge(s1, s2);
  }
  pair<long long, long long> query(long long l, long long r) {
    return query(l, r, 1, 1, siz);
  }
};
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  string S;
  long long q;
  cin >> S >> q;
  segtree st(S);
  while (q--) {
    long long l, r;
    cin >> l >> r;
    pair<long long, long long> it = st.query(l, r);
    cout << (r + 1 - l) - (it.first + it.second) << endl;
  }
  return 0;
}
