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;
#pragma comment(linker, "/STACK:16777216")
#pragma warning(disable : 4786)
struct node {
  int cnt, lf, rf;
  node() {}
  node(int _a, int _b, int _c) {
    cnt = _a;
    lf = _b;
    rf = _c;
  }
} v[4 * 1000009];
int n;
string a;
node merge(node a, node b) {
  node ret;
  memset(&ret, 0, sizeof(&ret));
  ret.cnt = a.cnt + b.cnt;
  int x = ((a.lf) < (b.rf) ? (a.lf) : (b.rf));
  if (a.lf && b.rf) {
    ret.cnt += x * 2;
  }
  ret.lf = a.lf + b.lf - x;
  ret.rf = a.rf + b.rf - x;
  return ret;
}
void insert(int idx, int st, int ed) {
  if (st == ed) {
    v[idx].cnt = 0;
    v[idx].lf = (a[st] == '(');
    v[idx].rf = (a[st] == ')');
    return;
  }
  int mid = (st + ed) / 2;
  if (st == 6 && ed == 8) st = st;
  insert(2 * idx, st, mid);
  insert(2 * idx + 1, mid + 1, ed);
  v[idx] = merge(v[2 * idx], v[2 * idx + 1]);
}
node query(int idx, int st, int ed, int s, int e) {
  if (st > e || ed < s) return node(0, 0, 0);
  if (st >= s && ed <= e) {
    return v[idx];
  }
  int mid = (st + ed) / 2;
  node a = query(2 * idx, st, mid, s, e);
  node b = query(2 * idx + 1, mid + 1, ed, s, e);
  node c = merge(a, b);
  return c;
}
int main() {
  ios_base::sync_with_stdio(0);
  int m, l, r;
  while (cin >> a) {
    memset(v, 0, sizeof(v));
    n = a.size();
    insert(1, 0, n - 1);
    cin >> m;
    while (m--) {
      cin >> l >> r;
      cout << query(1, 0, n - 1, l - 1, r - 1).cnt << endl;
      ;
    }
  }
  return 0;
}
