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 mod = 1e9 + 7;
const long long inf = 3e18 + 5;
int add(int a, int b) { return (a += b) < mod ? a : a - mod; }
int mul(int a, int b) { return 1LL * a * b % mod; }
int sub(int a, int b) { return (a -= b) < 0 ? a + mod : a; }
int ctz(int x) { return __builtin_ctz(x); }
int clz(int x) { return __builtin_clz(x); }
struct pt {
  int len, op, cl;
  pt() = default;
  pt(int a, int b, int c) : len(a), op(b), cl(c) {}
};
const int maxn = 1e6 + 6;
int n;
pt seg[4 * maxn], a[maxn];
void build(int l = 0, int r = n - 1, int i = 1) {
  if (l == r) {
    seg[i] = a[l];
    return;
  }
  int m = (l + r) / 2;
  build(l, m, i * 2);
  build(m + 1, r, i * 2 + 1);
  int mn = min(seg[i * 2].op, seg[i * 2 + 1].cl);
  seg[i].len = seg[i * 2].len + seg[i * 2 + 1].len + mn;
  seg[i].op = seg[i * 2].op + seg[i * 2 + 1].op - mn;
  seg[i].cl = seg[i * 2].cl + seg[i * 2 + 1].cl - mn;
}
pt qry(int tl, int tr, int l = 0, int r = n - 1, int i = 1) {
  if (l > tr) return pt(0, 0, 0);
  if (r < tl) return pt(0, 0, 0);
  if (tl <= l && tr >= r) {
    return seg[i];
  }
  int m = (l + r) / 2;
  pt L = qry(tl, tr, l, m, i * 2);
  pt R = qry(tl, tr, m + 1, r, i * 2 + 1);
  int mn = min(L.op, R.cl);
  return pt(L.len + R.len + mn, L.op + R.op - mn, L.cl + R.cl - mn);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  string s;
  cin >> s;
  n = int(s.size());
  for (int i = 0; i < n; i++) {
    if (s[i] == '(') {
      a[i] = pt(0, 1, 0);
    } else {
      a[i] = pt(0, 0, 1);
    }
  }
  build();
  int q;
  cin >> q;
  while (q--) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    cout << 2 * qry(l, r).len << "\n";
  }
}
