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;
using ll = long long;
ll md = 1000000007;
ll exp(ll a, ll b) {
  ll r = 1ll;
  while (b > 0) {
    if (b & 1) {
      r = r * (a % md);
      r = (r + md) % md;
    }
    b >>= 1;
    a = (a % md) * (a % md);
    a = (a + md) % md;
  }
  return (r + md) % md;
}
ll gcd(ll a, ll b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
ll Min(ll a, ll b) {
  if (a < b) return a;
  return b;
}
ll Max(ll a, ll b) {
  if (a > b) return a;
  return b;
}
const long long N = 1e6 + 5;
struct S {
  long long open, close, ans;
  S() { ans = -1; }
  void leaf(char c) {
    open = close = 0;
    if (c == '(')
      ++open;
    else
      ++close;
    ans = 0;
  }
};
long long n;
S t[2 * N];
S combine(S a, S b) {
  if (a.ans < 0) return b;
  if (b.ans < 0) return a;
  S c;
  long long x = Min(a.open, b.close);
  c.ans = a.ans + b.ans + x;
  c.open = a.open + b.open - x;
  c.close = a.close + b.close - x;
  return c;
}
void build() {
  for (long long i = n - 1; i > 0; i--)
    t[i] = combine(t[i << 1], t[i << 1 | 1]);
}
S query(long long l, long long r) {
  S resl, resr;
  for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
    if (l & 1) resl = combine(resl, t[l++]);
    if (r & 1) resr = combine(t[--r], resr);
  }
  return combine(resl, resr);
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  string s;
  cin >> s;
  n = s.size();
  for (ll i = 0; i <= n - 1; ++i) {
    t[i + n].leaf(s[i]);
  }
  build();
  long long q;
  cin >> q;
  while (q--) {
    long long l, r;
    cin >> l >> r;
    S ax = query(l - 1, r);
    cout << 2 * ax.ans << '\n';
  }
  return 0;
}
