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 int MAXN = 1123456;
struct node {
  int v, l, r;
  node() {}
  node(int x, int y, int z) {
    v = x;
    l = y;
    r = z;
  }
};
node combine(const node& l, const node& r) {
  int nv = min(l.r, r.l);
  return node(l.v + r.v + nv, l.l + r.l - nv, l.r + r.r - nv);
}
string s;
node st[4 * MAXN];
void build(int i, int l, int r) {
  if (l == r) {
    if (s[l] == '(')
      st[i] = node(0, 0, 1);
    else
      st[i] = node(0, 1, 0);
    return;
  }
  int m = (l + r) >> 1;
  int nxt = i << 1;
  build(nxt, l, m);
  build(nxt + 1, m + 1, r);
  st[i] = combine(st[nxt], st[nxt + 1]);
}
node query(int i, int l, int r, int ll, int rr) {
  if (rr < l || r < ll) return node(0, 0, 0);
  if (ll <= l && r <= rr) return st[i];
  int m = (l + r) >> 1;
  int nxt = i << 1;
  return combine(query(nxt, l, m, ll, rr), query(nxt + 1, m + 1, r, ll, rr));
}
int main() {
  cin >> s;
  build(1, 0, int(s.size()) - 1);
  int m;
  cin >> m;
  while (m--) {
    int x, y;
    cin >> x >> y;
    cout << query(1, 0, int(s.size()) - 1, x - 1, y - 1).v * 2 << '\n';
  }
  return 0;
}
