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;
template <typename T>
T ii() {
  T a;
  cin >> a;
  return a;
}
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
struct Node {
  int open, close, complete;
  Node(int open, int close, int complete) {
    this->open = open;
    this->close = close;
    this->complete = complete;
  }
};
const int MAX = 4 * (int)1e6;
string s;
vector<Node> dp(MAX, Node(0, 0, 0));
Node merge(Node a, Node b) {
  int additional = min(a.open, b.close);
  return Node(a.open + b.open - additional, a.close + b.close - additional,
              a.complete + b.complete + additional);
}
void build(int x, int l, int r) {
  if (l == r) {
    int open = s[l] == '(';
    int close = s[l] == ')';
    dp[x] = Node(open, close, 0);
    return;
  }
  int left = 2 * x + 1;
  int right = left + 1;
  int mid = l + r >> 1;
  build(left, l, mid);
  build(right, mid + 1, r);
  dp[x] = merge(dp[left], dp[right]);
}
Node query(int x, int l, int r, int ss, int se) {
  if (se < l || ss > r) return Node(0, 0, 0);
  if (l >= ss && r <= se) return dp[x];
  int mid = l + r >> 1;
  int left = 2 * x + 1;
  int right = left + 1;
  return merge(query(left, l, mid, ss, se), query(right, mid + 1, r, ss, se));
}
int main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> s;
  int n = s.length();
  build(0, 0, n - 1);
  int t;
  cin >> t;
  while (t--) {
    int l, r;
    cin >> l >> r;
    auto ans = query(0, 0, n - 1, l - 1, r - 1);
    cout << (ans.complete << 1) << "\n";
  }
  return 0;
}
