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 long long int MOD = 1e9 + 7;
const long double PI = 3.14159265;
long long int powerWithMod(long long int base, long long int exponent,
                           long long int modulus = LLONG_MAX) {
  long long int result = 1;
  base %= modulus;
  while (exponent > 0) {
    if (exponent % 2 == 1) result = (result * base) % modulus;
    exponent >>= 1;
    base = (base * base) % modulus;
  }
  return result;
}
long long int modInverse(long long int a, long long int m = MOD) {
  return powerWithMod(a, m - 2, m);
}
struct node {
  int maxlen, open, close;
  node() : maxlen(0), open(0), close(0) {}
  static node combine(node& a, node& b) {
    node ans;
    int temp = min(a.open, b.close);
    ans.maxlen = a.maxlen + b.maxlen + 2 * temp;
    ans.open = a.open + b.open - temp;
    ans.close = a.close + b.close - temp;
    return ans;
  }
};
const int MAXN = 1e6 + 5;
int n, l, r;
string s;
node a[2 * MAXN];
inline void build() {
  for (int i = s.size() - 1; i > 0; i--)
    a[i] = node::combine(a[i << 1], a[i << 1 | 1]);
}
int query(int l, int r) {
  node ansl, ansr;
  l += s.size();
  r += s.size();
  for (; l < r; l >>= 1, r >>= 1) {
    if (l & 1) ansl = node::combine(ansl, a[l++]);
    if (r & 1) ansr = node::combine(a[--r], ansr);
  }
  return node::combine(ansl, ansr).maxlen;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> s;
  for (int i = 0; i < s.size(); i++) {
    a[i + s.size()].open = (s[i] == '(');
    a[i + s.size()].close = 1 ^ a[i + s.size()].open;
  }
  build();
  cin >> n;
  while (n--) {
    cin >> l >> r;
    cout << query(l - 1, r) << "\n";
  }
  return 0;
}
