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 X, Y, ans;
};
string S;
node segtree[4000000];
node merge(node L, node R) {
  int add_length = min(L.X, R.Y);
  node N = {L.X - add_length + R.X, L.Y + R.Y - add_length,
            L.ans + R.ans + 2 * add_length};
  return N;
}
void build_tree(int L, int R, int i) {
  if (L == R) {
    segtree[i] = {0, 0, 0};
    if (S[L] == '(')
      segtree[i].X++;
    else
      segtree[i].Y++;
    return;
  }
  int mid = (L + R) / 2;
  build_tree(L, mid, 2 * i + 1);
  build_tree(mid + 1, R, 2 * i + 2);
  segtree[i] = merge(segtree[2 * i + 1], segtree[2 * i + 2]);
}
node query(int L, int R, int A, int B, int i) {
  if (L > R || L > B || R < A) return node();
  if (A <= L && R <= B) return segtree[i];
  int mid = (L + R) / 2;
  return merge(query(L, mid, A, B, 2 * i + 1),
               query(mid + 1, R, A, B, 2 * i + 2));
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> S;
  int N = S.length();
  build_tree(0, N - 1, 0);
  int Q;
  cin >> Q;
  while (Q--) {
    int L, R;
    cin >> L >> R;
    L--;
    R--;
    cout << query(0, N - 1, L, R, 0).ans << endl;
  }
}
