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;
char s[1000010];
struct Node {
  int left, right, match, x, y;
} node[1000010 * 4];
struct SegTree {
  void create(int x, int y, int root = 1) {
    node[root].x = x, node[root].y = y;
    if (x == y) {
      node[root].match = 0;
      if (s[x] == '(') {
        node[root].left = 1, node[root].right = 0;
      } else {
        node[root].left = 0, node[root].right = 1;
      }
    } else {
      create(x, (x + y) / 2, root * 2);
      create((x + y) / 2 + 1, y, root * 2 + 1);
      int c = min(node[root * 2].left, node[root * 2 + 1].right);
      node[root].match = node[root * 2].match + node[root * 2 + 1].match + c;
      node[root].left = node[root * 2].left + node[root * 2 + 1].left - c;
      node[root].right = node[root * 2].right + node[root * 2 + 1].right - c;
    }
  }
  int search(int x, int y, int &left, int &right, int root = 1) {
    if (x <= node[root].x && node[root].y <= y) {
      left = node[root].left, right = node[root].right;
      return node[root].match;
    }
    if (x > node[root].y || y < node[root].x) {
      left = right = 0;
      return 0;
    }
    int lleft, lright, rleft, rright, match;
    match = search(x, y, lleft, lright, root * 2) +
            search(x, y, rleft, rright, root * 2 + 1);
    int c = min(lleft, rright);
    left = lleft + rleft - c;
    right = lright + rright - c;
    return match + c;
  }
} tree;
int main() {
  scanf("%s", s + 1);
  int n = strlen(s + 1);
  tree.create(1, n);
  int m, x, y, left, right;
  cin >> m;
  for (int i = 0; i < m; ++i) {
    cin >> x >> y;
    cout << tree.search(x, y, left, right) * 2 << endl;
  }
  return 0;
}
