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 inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3f;
const int modulo = 1e9 + 7;
struct node {
  int n, a, b;
};
const int M = (1 << 20);
node tree[2 * M + 5];
node check(node left, node right) {
  node curr;
  int newnum = 0;
  if (left.b > 0 && right.a > 0) {
    if (left.b > right.a) {
      newnum = right.a;
      left.b -= newnum;
      right.a = 0;
    } else {
      newnum = left.b;
      right.a -= newnum;
      left.b = 0;
    }
  }
  curr.a = left.a + right.a;
  curr.b = left.b + right.b;
  curr.n = newnum + left.n + right.n;
  return curr;
}
int query(int l, int r) {
  int res = 0;
  l += M - 1;
  r += M - 1;
  node left = {0, 0, 0};
  node right = {0, 0, 0};
  while (l <= r) {
    if (l % 2) {
      node curr_left = tree[l++];
      left = check(left, curr_left);
    }
    if (r % 2 == 0) {
      node curr_right = tree[r--];
      right = check(curr_right, right);
    }
    l /= 2;
    r /= 2;
  }
  res = check(left, right).n;
  return 2 * res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  string s;
  cin >> s;
  for (int i = 0; i < ((int)s.size()); ++i) {
    if (s[i] == '(') {
      node a = {0, 0, 1};
      tree[i + M] = a;
    } else {
      node a = {0, 1, 0};
      tree[i + M] = a;
    }
  }
  for (int i = M - 1; i >= 1; --i) {
    node left = tree[2 * i];
    node right = tree[2 * i + 1];
    tree[i] = check(left, right);
  }
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) {
    int a, b;
    cin >> a >> b;
    cout << query(a, b) << "\n";
  }
  return 0;
}
