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 N = 1e6;
struct node {
  int len;
  int open, close;
  node() { len = open = close = 0; }
  node(int a, int b, int c) {
    len = a;
    open = b;
    close = c;
  }
};
string s;
node segTree[4 * N];
void build(int l, int r, int num) {
  if (l > r) return;
  if (l == r) {
    segTree[num] = (s[l] == ')' ? node(0, 0, 1) : node(0, 1, 0));
    return;
  }
  int mid = l + r >> 1;
  int left = num << 1, right = left | 1;
  build(l, mid, left);
  build(mid + 1, r, right);
  int diff = min(segTree[left].open, segTree[right].close);
  segTree[num].len = segTree[left].len + segTree[right].len + diff;
  segTree[num].open = segTree[left].open + segTree[right].open - diff;
  segTree[num].close = segTree[left].close + segTree[right].close - diff;
}
node query(int l, int r, int num, int lq, int rq) {
  if (l > r) return node(0, 0, 0);
  if (lq > r || rq < l) return node(0, 0, 0);
  if (l >= lq && r <= rq) return segTree[num];
  int mid = l + r >> 1;
  int left = num << 1, right = left | 1;
  node lres = query(l, mid, left, lq, rq);
  node rres = query(mid + 1, r, right, lq, rq);
  int diff = min(lres.open, rres.close);
  return node(lres.len + rres.len + diff, lres.open + rres.open - diff,
              lres.close + rres.close - diff);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> s;
  int n = s.size();
  build(0, n - 1, 1);
  int q;
  cin >> q;
  while (q--) {
    int l, r;
    cin >> l >> r;
    node res = query(0, n - 1, 1, l - 1, r - 1);
    cout << (res.len << 1) << endl;
  }
}
