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 + 5;
string s;
class segment_tree {
 public:
  int left, right, pairs;
  segment_tree() { left = right = pairs = 0; }
} tree[N << 2];
void build(int l, int r, int x) {
  if (l == r) {
    tree[x].left = (s[l - 1] == '(');
    tree[x].right = (s[l - 1] == ')');
  } else {
    int mid = l + r >> 1, lc = x + x, rc = lc + 1, let;
    build(l, mid, lc);
    build(mid + 1, r, rc);
    let = min(tree[lc].left, tree[rc].right);
    tree[x].pairs += let + tree[lc].pairs + tree[rc].pairs;
    tree[x].left = tree[lc].left + tree[rc].left - let;
    tree[x].right = tree[lc].right + tree[rc].right - let;
  }
}
segment_tree query(int l, int r, int ql, int qr, int x) {
  if (qr < l || r < ql) {
    segment_tree now;
    return now;
  }
  if (ql <= l && r <= qr) return tree[x];
  int mid = l + r >> 1, lc = x + x, rc = lc + 1;
  segment_tree L = query(l, mid, ql, qr, lc);
  segment_tree R = query(mid + 1, r, ql, qr, rc);
  segment_tree let;
  int temp = 0;
  temp = min(L.left, R.right);
  let.pairs = temp + L.pairs + R.pairs;
  let.left = L.left + R.left - temp;
  let.right = L.right + R.right - temp;
  return let;
}
signed main() {
  int q, l, r;
  cin >> s;
  build(1, s.size(), 1);
  cin >> q;
  while (q--) {
    cin >> l >> r;
    segment_tree temp = query(1, s.size(), l, r, 1);
    cout << (temp.pairs << 1) << '\n';
  }
  return 0;
}
