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 MAXN = 1e6 + 9;
char s[MAXN];
struct node {
  int ans;
  int opening;
  int closing;
} segTree[4 * MAXN], shit;
void merge(node& mergeInto, const node& a, const node& b) {
  int mina = min(a.opening, b.closing);
  mergeInto.ans = a.ans + b.ans + mina;
  mergeInto.opening = a.opening + b.opening - mina;
  mergeInto.closing = a.closing + b.closing - mina;
}
void build_tree(int v, int l, int r) {
  if (l == r) {
    if (s[l] == '(') {
      segTree[v].opening = 1;
      segTree[v].closing = segTree[v].ans = 0;
    } else {
      segTree[v].closing = 1;
      segTree[v].opening = segTree[v].ans = 0;
    }
    return;
  }
  int mid = (l + r) >> 1;
  build_tree(2 * v, l, mid);
  build_tree(2 * v + 1, mid + 1, r);
  merge(segTree[v], segTree[2 * v], segTree[2 * v + 1]);
}
node query(int v, int l, int r, int start, int end) {
  if (l > r || l > end || r < start) {
    return shit;
  }
  if (l >= start && r <= end) {
    return segTree[v];
  }
  int mid = (l + r) >> 1;
  node res;
  merge(res, query(2 * v, l, mid, start, end),
        query(2 * v + 1, mid + 1, r, start, end));
  return res;
}
int main(int argc, char const* argv[]) {
  scanf("%s", s);
  int n = strlen(s);
  build_tree(1, 0, n - 1);
  int m;
  scanf("%d", &m);
  shit.ans = shit.opening = shit.closing = 0;
  while (m--) {
    int l, r;
    scanf("%d%d", &l, &r);
    l--;
    r--;
    printf("%d\n", 2 * query(1, 0, n - 1, l, r).ans);
  }
  return 0;
}
