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;
string second;
int n, l, r;
struct node {
  int a, b, c;
} st[4000001];
node comp(node A, node B) {
  node ans;
  int X = min(A.b, B.c);
  ans.a = A.a + B.a + X * 2;
  ans.b = A.b + B.b - X;
  ans.c = A.c + B.c - X;
  return ans;
}
void build(int v, int l, int r) {
  if (l == r) {
    if (second[l - 1] == '(')
      st[v].b = 1;
    else
      st[v].c = 1;
    return;
  }
  int mid = (l + r) / 2;
  build(v * 2, l, mid);
  build(v * 2 + 1, mid + 1, r);
  st[v] = comp(st[v * 2], st[v * 2 + 1]);
}
node qr(int v, int A, int B, int l, int r) {
  node ans;
  ans.a = ans.b = ans.c = 0;
  if (l > B || r < A) return ans;
  if (A == l && B == r) return st[v];
  int mid = (A + B) / 2;
  node L = qr(v * 2, A, mid, l, min(mid, r));
  node R = qr(v * 2 + 1, mid + 1, B, max(mid + 1, l), r);
  return comp(L, R);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> second;
  cin >> n;
  build(1, 1, second.length());
  while (n--) {
    cin >> l >> r;
    cout << qr(1, 1, second.length(), l, r).a << endl;
  }
  return 0;
}
