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 cell {
  int a;
  int b;
  int c;
};
const int MAX_N = 1000005;
int n;
cell A[MAX_N * 2];
cell combine(cell &c1, cell &c2) {
  cell nc;
  int t = min(c1.b, c2.c);
  nc.a = c1.a + c2.a + t;
  nc.b = c1.b + c2.b - t;
  nc.c = c1.c + c2.c - t;
  return nc;
}
void build() {
  for (int i = n - 1; i > 0; i--) {
    A[i] = combine(A[i * 2], A[i * 2 + 1]);
  }
}
int query(int l, int r) {
  cell resl, resr;
  resl.a = resl.b = resl.c = resr.a = resr.b = resr.c = 0;
  for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
    if (l & 1) {
      resl = combine(resl, A[l++]);
    }
    if (r & 1) {
      resr = combine(A[--r], resr);
    }
  }
  return combine(resl, resr).a * 2;
}
int main() {
  string s;
  cin >> s;
  n = s.size();
  for (int i = 0; i < s.size(); i++) {
    cell nc;
    nc.a = nc.b = nc.c = 0;
    char c = s[i];
    if (c == '(') {
      nc.b = 1;
    } else {
      nc.c = 1;
    }
    A[i + n] = nc;
  }
  build();
  int m;
  scanf("%d", &m);
  for (int i = 0; i < m; i++) {
    int a, b;
    scanf("%d %d", &a, &b);
    printf("%d\n", query(a - 1, b));
  }
  return 0;
}
