You are given a bracket sequence s consisting of n opening '(' and closing ')' brackets.

A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.

You can change the type of some bracket s_i. It means that if s_i =  ')' then you can change it to '(' and vice versa.

Your task is to calculate the number of positions i such that if you change the type of the i-th bracket, then the resulting bracket sequence becomes regular.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 10^6) — the length of the bracket sequence.

The second line of the input contains the string s consisting of n opening '(' and closing ')' brackets.

Output

Print one integer — the number of positions i such that if you change the type of the i-th bracket, then the resulting bracket sequence becomes regular.

Examples

Input


6
(((())


Output


3


Input


6
()()()


Output


0


Input


1
)


Output


0


Input


8
)))(((((


Output


0
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e6 + 6;
int n;
char s[maxn];
int now;
struct node {
  int lpos, rpos;
} p[maxn << 2];
void pushup(int pos) {
  p[pos].lpos = p[pos << 1].lpos;
  p[pos].rpos = p[pos << 1 | 1].rpos;
  if (p[pos << 1].rpos < p[pos << 1 | 1].lpos) {
    p[pos].lpos += p[pos << 1 | 1].lpos - p[pos << 1].rpos;
  } else {
    p[pos].rpos += p[pos << 1].rpos - p[pos << 1 | 1].lpos;
  }
}
void build(int pos, int l, int r) {
  if (l == r) {
    p[pos].lpos = s[l] == ')';
    p[pos].rpos = !p[pos].lpos;
    return;
  }
  int mid = l + r >> 1;
  build(pos << 1, l, mid);
  build(pos << 1 | 1, mid + 1, r);
  pushup(pos);
}
void update(int pos, int l, int r) {
  if (l == r) {
    p[pos].lpos = !p[pos].lpos;
    p[pos].rpos = !p[pos].rpos;
    return;
  }
  int mid = l + r >> 1;
  if (mid >= now) {
    update(pos << 1, l, mid);
  } else
    update(pos << 1 | 1, mid + 1, r);
  pushup(pos);
}
int main() {
  scanf("%d", &n);
  scanf("%s", s + 1);
  build(1, 1, n);
  int res = 0;
  for (int i = 1; i <= n; ++i) {
    now = i;
    update(1, 1, n);
    if (p[1].lpos == p[1].rpos && p[1].rpos == 0) res++;
    update(1, 1, n);
  }
  printf("%d\n", res);
  return 0;
}
