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;
int n;
string s;
struct SegmentTree {
  int low, high, mid;
  int openLeft, closeLeft, res;
  SegmentTree *left, *right;
  SegmentTree() {}
  SegmentTree(int low, int high) {
    this->low = low;
    this->high = high;
    mid = (low + high) / 2;
    if (low == high) {
      left = right = NULL;
      openLeft = (s[low] == '(');
      closeLeft = (s[low] == ')');
      res = 0;
    } else {
      left = new SegmentTree(low, mid);
      right = new SegmentTree(mid + 1, high);
      int newPairs = min(left->openLeft, right->closeLeft);
      res = left->res + right->res + newPairs;
      openLeft = left->openLeft + right->openLeft - newPairs;
      closeLeft = left->closeLeft + right->closeLeft - newPairs;
    }
  }
  int get(int x, int y, int &open, int &close) {
    if (low == x && high == y) {
      open = openLeft;
      close = closeLeft;
      return res;
    }
    int resL = 0, openL = 0, closeL = 0, resR = 0, openR = 0, closeR = 0;
    if (x <= mid) resL = left->get(x, min(y, mid), openL, closeL);
    if (mid < y) resR = right->get(max(x, mid + 1), y, openR, closeR);
    int newPairs = min(openL, closeR);
    open = openL + openR - newPairs;
    close = closeL + closeR - newPairs;
    return resL + resR + newPairs;
  }
};
int main() {
  ios::sync_with_stdio(0);
  cin >> s;
  SegmentTree *root = new SegmentTree(0, s.size() - 1);
  int Q, x, y, z, t;
  cin >> Q;
  while (Q--) {
    cin >> x >> y;
    cout << root->get(--x, --y, z, t) * 2 << endl;
  }
}
