#include <stdio.h>

int N;
char S[100100];

int main()
{
	scanf ("%d %s",&N,S+1);

	long long ab = 0, amn = 0, b = 0, mn = 0;
	for (int i=1;i<=N;i++){
		if (S[i] == '(') b++;
		else{
			b--;
			if (mn > b) mn = b;
		}

		if (amn > ab + mn)
			amn = ab + mn;
		ab += b;
	}

	long long len = (long long)N * (N + 1) / 2 - ab + 2 * amn;
	printf ("%lld\n",len);

	return 0;
}