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 input;
int n, m;
int ql, qr;
int ans;
struct node {
  pair<int, int> lr;
  int ans;
};
node segTree[4000000];
pair<int, int> query(int left, int right, int pos) {
  node curNode = segTree[pos];
  pair<int, int> p;
  if (ql > right || qr < left) {
    p.first = 0;
    p.second = 0;
    return p;
  }
  if (left >= ql && right <= qr) {
    ans += curNode.ans;
    p.first = curNode.lr.first - curNode.ans;
    p.second = curNode.lr.second - curNode.ans;
    return p;
  }
  int mid = left + (right - left) / 2;
  pair<int, int> l = query(left, mid, 2 * pos + 1);
  pair<int, int> r = query(mid + 1, right, 2 * pos + 2);
  int mn = min(l.first, r.second);
  ans = ans + mn;
  p.first = r.first + l.first - mn;
  p.second = l.second + r.second - mn;
  return p;
}
void build(int left, int right, int segmentTreePosition) {
  node newNode;
  if (left == right) {
    newNode.ans = 0;
    if (input[left] == '(') {
      newNode.lr.first = 1;
      newNode.lr.second = 0;
    } else {
      newNode.lr.first = 0;
      newNode.lr.second = 1;
    }
    segTree[segmentTreePosition] = newNode;
    return;
  }
  int mid = left + (right - left) / 2;
  int leftChildPos = 2 * segmentTreePosition + 1;
  int rightChildPos = 2 * segmentTreePosition + 2;
  build(left, mid, leftChildPos);
  build(mid + 1, right, rightChildPos);
  node leftChildNode = segTree[leftChildPos];
  node rightChildNode = segTree[rightChildPos];
  newNode.lr.first = leftChildNode.lr.first + rightChildNode.lr.first;
  newNode.lr.second = leftChildNode.lr.second + rightChildNode.lr.second;
  newNode.ans = leftChildNode.ans + rightChildNode.ans +
                min(leftChildNode.lr.first - leftChildNode.ans,
                    rightChildNode.lr.second - rightChildNode.ans);
  segTree[segmentTreePosition] = newNode;
}
int main() {
  cin >> input;
  n = input.size();
  build(0, n - 1, 0);
  cin >> m;
  for (int i = 0; i < m; i++) {
    cin >> ql >> qr;
    ql--;
    qr--;
    ans = 0;
    query(0, n - 1, 0);
    cout << 2 * ans << endl;
  }
  return 0;
}
