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;
long double PI = acosl(-1);
bool compare_int(int a, int b) { return (a > b); }
bool compare_string(string a, string b) { return a.size() < b.size(); }
bool compare_pair(const pair<int, int> &a, const pair<int, int> &b) {
  if (a.second == b.second)
    return a.first < b.first;
  else
    return (a.second > b.second);
}
bool cmp(pair<string, int> x, pair<string, int> y) {
  return x.second < y.second;
}
void NA() {
  cout << "NO" << endl;
  exit(0);
}
void YA() {
  cout << "YES" << endl;
  exit(0);
}
string s;
struct info {
  int open, close, len;
};
info tr[4 * 1000006];
info Merge(info l, info r) {
  info m;
  if (l.open >= r.close) {
    m.close = l.close;
    m.open = r.open + (l.open - r.close);
    m.len = l.len + r.len + r.close * 2;
  } else {
    m.open = r.open;
    m.close = l.close + (r.close - l.open);
    m.len = l.len + r.len + l.open * 2;
  }
  return m;
}
void build(int u, int b, int e) {
  if (b == e) {
    if (s[b - 1] == '(')
      tr[u].open = 1;
    else
      tr[u].close = 1;
    return;
  }
  int mid = (b + e) >> 1;
  build(2 * u, b, mid);
  build(2 * u + 1, mid + 1, e);
  tr[u] = Merge(tr[2 * u], tr[2 * u + 1]);
}
info query(int u, int b, int e, int i, int j) {
  if (e < i or b > j) return {0, 0, 0};
  if (b >= i and e <= j) return tr[u];
  int mid = (b + e) >> 1;
  info l = query(2 * u, b, mid, i, j);
  info r = query(2 * u + 1, mid + 1, e, i, j);
  return Merge(l, r);
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> s;
  int len = s.size();
  build(1, 1, len);
  int n, x, y;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> x >> y;
    info res = query(1, 1, len, x, y);
    cout << res.len << endl;
  }
}
