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;
struct node {
  int open, close;
  node() { open = 0, close = 0; }
  node(char ch) {
    if (ch == '(') {
      open = 1;
      close = 0;
    } else {
      open = 0;
      close = 1;
    }
  }
  void merge(node left, node right) {
    int match = min(left.open, right.close);
    open = left.open + right.open - match;
    close = left.close + right.close - match;
  }
};
vector<char> a;
vector<node> tree;
void build(int ind, int l, int r) {
  if (l == r) {
    tree[ind] = node(a[l]);
    return;
  }
  int mid = (l + r) / 2;
  build(2 * ind, l, mid);
  build(2 * ind + 1, mid + 1, r);
  tree[ind].merge(tree[2 * ind], tree[2 * ind + 1]);
}
node query(int ind, int l, int r, int x, int y) {
  if (l == x & r == y) {
    return tree[ind];
  }
  int mid = (l + r) / 2;
  if (y <= mid)
    return query(2 * ind, l, mid, x, y);
  else if (x > mid)
    return query(2 * ind + 1, mid + 1, r, x, y);
  else {
    node tmp1, tmp2, tmp;
    tmp1 = query(2 * ind, l, mid, x, mid);
    tmp2 = query(2 * ind + 1, mid + 1, r, mid + 1, y);
    tmp.merge(tmp1, tmp2);
    return tmp;
  }
}
int main() {
  string s;
  cin >> s;
  int t, n = s.size();
  a.resize(n);
  tree.resize(4 * n);
  for (int i = 0; i < n; i++) {
    a[i] = s[i];
  }
  build(1, 0, n - 1);
  cin >> t;
  while (t--) {
    int x, y;
    cin >> x >> y;
    node tmp = query(1, 0, n - 1, x - 1, y - 1);
    cout << y - x + 1 - tmp.close - tmp.open << endl;
  }
}
