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;
const int N = 1e6 + 5;
char s[N];
struct node {
  int a = 0, b = 0, c = 0;
  node() : a(0), b(0), c(0) {}
  node(node l, node r) {
    int t = min(l.b, r.c);
    a = (l.a + r.a + t);
    b = (l.b + r.b - t);
    c = (l.c + r.c - t);
  }
} tree[N << 2];
void build(int ind, int l, int r) {
  if (l == r) {
    s[l] == '(' ? tree[ind].b++ : tree[ind].c++;
    return;
  }
  int mid = (l + r) >> 1;
  build(ind << 1, l, mid);
  build(ind << 1 | 1, mid + 1, r);
  tree[ind] = node(tree[ind << 1], tree[ind << 1 | 1]);
}
node get(int ind, int l, int r, int s, int e) {
  if (e < l or s > r) return node();
  if (l >= s and r <= e) return tree[ind];
  int mid = (l + r) >> 1;
  return node(get(ind << 1, l, mid, s, e), get(ind << 1 | 1, mid + 1, r, s, e));
}
int main() {
  scanf("%s", s);
  int l, r, m, n = strlen(s);
  build(1, 0, n - 1);
  scanf("%d", &m);
  for (int i = 0; i < m; i++) {
    scanf("%d%d", &l, &r);
    printf("%d\n", get(1, 0, n - 1, --l, --r).a << 1);
  }
  return 0;
}
