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 inf = 1e9 + 5;
const long long infll = 1e18 + 5ll;
const long double eps = 1e-15;
const int maxn = 1e6 + 100;
const int maxlog = 21;
const int P = 97;
const int mod = 1e9 + 7;
int n;
string second;
struct ez {
  int zer, one, ans, val;
  ez() {
    zer = one = ans = 0;
    val = -1;
  }
  ez(int _val) {
    if (_val == 0)
      zer = 1, one = 0;
    else
      one = 1, zer = 0;
    ans = 0;
    val = _val;
  }
} t[maxn * 4];
ez combine(ez a, ez b) {
  ez ret;
  int kek = min(a.zer, b.one);
  ret.ans = a.ans + b.ans + kek;
  a.zer -= kek;
  b.one -= kek;
  ret.zer = a.zer + b.zer;
  ret.one = b.one + a.one;
  return ret;
}
ez lol() {
  ez ret;
  ret.one = ret.zer = ret.ans = 0;
  ret.val = -1;
  return ret;
}
void show(int v = 1, int tl = 1, int tr = n) {
  if (tl == tr) {
    cout << t[v].ans;
    return;
  }
  int tm = (tl + tr) >> 1;
  show(v + v, tl, tm);
  show(v + v + 1, tm + 1, tr);
}
void build(int v = 1, int tl = 1, int tr = n) {
  if (tl == tr) {
    t[v] = ez((second[tl] == '(' ? 0 : 1));
    return;
  }
  int tm = (tl + tr) >> 1;
  build(v + v, tl, tm);
  build(v + v + 1, tm + 1, tr);
  t[v] = combine(t[v + v], t[v + v + 1]);
}
ez query(int l, int r, int v = 1, int tl = 1, int tr = n) {
  if (l > tr || r < tl) return lol();
  if (l <= tl && tr <= r) return t[v];
  int tm = (tl + tr) >> 1;
  return combine(query(l, r, v + v, tl, tm),
                 query(l, r, v + v + 1, tm + 1, tr));
}
int main() {
  int q;
  cin >> second >> q;
  n = second.size();
  second = "?" + second;
  build();
  for (int i = 1, l, r; i <= q; ++i) {
    cin >> l >> r;
    cout << query(l, r).ans * 2 << '\n';
  }
  return 0;
}
