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 <class T>
inline T gcd(T a, T b) {
  return (!b ? a : gcd(b, a % b));
}
template <class T>
inline T ABS(T x) {
  return ((x) > 0 ? (x) : (-(x)));
}
const int N = 1000010;
string str;
int bopen[N << 2];
int bclose[N << 2];
int ans[N << 2];
int ANS;
struct pii {
  int open;
  int close;
};
void init(int b, int e, int curr) {
  if (b == e) {
    if (str[b - 1] == '(') {
      bopen[curr] = 1;
      bclose[curr] = 0;
    } else {
      bopen[curr] = 0;
      bclose[curr] = 1;
    }
    return;
  }
  int m = (b + e) >> 1;
  int lc = curr << 1;
  int rc = lc + 1;
  init(b, m, lc), init(m + 1, e, rc);
  int bopen_lc = bopen[lc];
  int bclose_rc = bclose[rc];
  if (bopen[lc] <= bclose[rc]) {
    bclose_rc -= bopen[lc];
    bopen_lc = 0;
  } else {
    bopen_lc -= bclose[rc];
    bclose_rc = 0;
  }
  bopen[curr] = bopen_lc + bopen[rc];
  bclose[curr] = bclose[lc] + bclose_rc;
  ans[curr] = (min(bopen[lc], bclose[rc]) << 1) + ans[lc] + ans[rc];
}
inline pii query(int b, int e, int qb, int qe, int curr) {
  if (qe < b || qb > e) {
    pii ret;
    ret.open = ret.close = 0;
    return ret;
  }
  if (b >= qb && e <= qe) {
    ::ANS += ans[curr];
    pii ret;
    ret.open = bopen[curr];
    ret.close = bclose[curr];
    return ret;
  }
  int m = (b + e) >> 1;
  int lc = curr << 1;
  int rc = lc + 1;
  pii Left = query(b, m, qb, qe, lc);
  pii Right = query(m + 1, e, qb, qe, rc);
  int mn = min(Left.open, Right.close);
  ::ANS += (mn << 1);
  if (Left.open == mn) {
    Left.open = 0;
    Right.close -= mn;
  } else {
    Right.close = 0;
    Left.open -= mn;
  }
  pii ret;
  ret.open = Left.open + Right.open;
  ret.close = Left.close + Right.close;
  return ret;
}
int main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cin >> ::str;
  int n = int((::str).size());
  init(1, n, 1);
  int qq;
  cin >> qq;
  while (qq--) {
    int ll, rr;
    cin >> ll >> rr;
    ::ANS = 0;
    query(1, n, ll, rr, 1);
    cout << ::ANS << '\n';
  }
}
