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 mod = 1e9 + 7;
long long int opbrackets[5000005];
long long int clbrackets[5000005];
long long int segtree[5000005];
string s;
void build_brackets(long long int node, long long int tl, long long int tr) {
  if (tl == tr) {
    char ch = s[tl];
    if (ch == '(') {
      opbrackets[node] = 1;
      clbrackets[node] = 0;
    } else {
      opbrackets[node] = 0;
      clbrackets[node] = 1;
    }
  } else {
    long long int mid = (tl + tr) / 2;
    build_brackets(2 * node, tl, mid);
    build_brackets(2 * node + 1, mid + 1, tr);
    opbrackets[node] = opbrackets[2 * node] + opbrackets[(2 * node) + 1];
    clbrackets[node] = clbrackets[2 * node] + clbrackets[(2 * node) + 1];
  }
}
void build(long long int node, long long int tl, long long int tr) {
  if (tl == tr) {
    segtree[node] = 0;
  } else {
    long long int mid = (tl + tr) / 2;
    build(2 * node, tl, mid);
    build(2 * node + 1, mid + 1, tr);
    segtree[node] =
        segtree[2 * node] + segtree[(2 * node) + 1] +
        (2 * min(opbrackets[2 * node] - (segtree[2 * node] / 2),
                 clbrackets[(2 * node) + 1] - (segtree[(2 * node) + 1] / 2)));
  }
}
long long int query_opbrackets(long long int node, long long int tl,
                               long long int tr, long long int ql,
                               long long int qr) {
  if (ql > qr)
    return 0;
  else if ((ql == tl) and (qr == tr)) {
    return opbrackets[node];
  } else {
    long long int mid = (tl + tr) / 2;
    long long int l = query_opbrackets(2 * node, tl, mid, ql, min(qr, mid));
    long long int r =
        query_opbrackets(2 * node + 1, mid + 1, tr, max(mid + 1, ql), qr);
    return (l + r);
  }
}
long long int query_clbrackets(long long int node, long long int tl,
                               long long int tr, long long int ql,
                               long long int qr) {
  if (ql > qr)
    return 0;
  else if ((ql == tl) and (qr == tr)) {
    return clbrackets[node];
  } else {
    long long int mid = (tl + tr) / 2;
    long long int l = query_clbrackets(2 * node, tl, mid, ql, min(qr, mid));
    long long int r =
        query_clbrackets(2 * node + 1, mid + 1, tr, max(mid + 1, ql), qr);
    return (l + r);
  }
}
long long int query(long long int node, long long int tl, long long int tr,
                    long long int ql, long long int qr) {
  if (ql > qr)
    return 0;
  else if ((ql == tl) and (qr == tr)) {
    return segtree[node];
  } else {
    long long int mid = (tl + tr) / 2;
    long long int l1 = query_opbrackets(2 * node, tl, mid, ql, min(qr, mid));
    long long int r1 =
        query_clbrackets(2 * node + 1, mid + 1, tr, max(ql, mid + 1), qr);
    long long int l2 = query(2 * node, tl, mid, ql, min(qr, mid));
    long long int r2 = query(2 * node + 1, mid + 1, tr, max(ql, mid + 1), qr);
    long long int a = l2 + r2;
    long long int b = 2 * min(l1 - (l2 / 2), r1 - (r2 / 2));
    return (a + b);
  }
}
void Compute(string s) {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int n = s.length();
  build_brackets(1, 0, n - 1);
  build(1, 0, n - 1);
  long long int q;
  cin >> q;
  for (long long int i = 0; i < q; i++) {
    long long int ql, qr;
    cin >> ql >> qr;
    ql--;
    qr--;
    long long int ans = query(1, 0, n - 1, ql, qr);
    cout << ans << "\n";
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> s;
  Compute(s);
}
