#include <iostream>
#include <string>
#include <map>
#include  <vector>
#include  <unordered_map>
#include  <memory>
#include  <utility>
#include  <list>
#include <cstring>
#include  <functional>
#include <algorithm>

using namespace std;

#define N
#define M
#define WATCH(x) cout << (#x) << ": " << (x) << endl
#define fWATCH(x, y) cout << x << ": " << y << endl
#define tWATCH(x, y, z) cout << x << ": " << y  << ", " << z << endl
#define INFO(x) cout << "[ " << x << " ]\n"
#define nINFO(n, x) cout << "[ " << to_string() << ": " << x << " ]\n"


#define SUM(vec, fn) accumulate(vec.begin(), vec.end(), 0, fn)

template <typename T1, typename T2>
struct Pair {
	T1 x; T2 y;
};

struct Range {
	int from; int to;
};

using Str = string;
template <typename T> using Vec = vector<T>;
using StrVec = vector<string>;
using nMap = map<int, Str>;
template <typename Key, typename T>
using xMap  = map<Key, T>;

// #define FOR(from, to, what) for (auto i = from; i < to; i++) { what(i); }
// #define FOR(from, to, from2, to2, what) for (auto j = from; j < to; j++) { for (auto i = from; i < to; i++) { what(i, j); } }

typedef long int32;
typedef unsigned long uint32;
typedef long long ll;
typedef unsigned long long uint64;

#define toS(x) to_string(x)

typedef struct Node {
	Node * left = nullptr;
	Node * right = nullptr;
	Node * parent = nullptr;
	int value = 1;
} Node;

int solve(Node * root)
{
	if(root->left != nullptr && root->right != nullptr)
	{
		return solve(root->left) * solve(root->right);
	}

	if(root->left != nullptr && root->right == nullptr)
	{
		root->value = 1 + solve(root->left);
	}
	
	return root->value;
}

int main()
{
	int n;
	cin >> n;
	string brackets;
	cin >> brackets;
	
	char slice[3];
	slice[2] = '\0';
	int acc = 0;
	int acc2 = 0;

	Node * root = new Node();
	// building tree
	for(size_t i = 0; i < brackets.size(); i++)
	{
		if(brackets[i] == '(') {
			if(root->left == nullptr)
			{
				root->left = new Node();
				root->left->parent = root;
				root = root->left;
			}
			else
			{
				root->right = new Node();
				root->right->parent = root;
				root = root->right;
			}
		}
		else if(brackets[i] == ')')
		{
			root = root->parent;
		}
	}
	
	cout << solve(root) << endl;


	/*for (size_t i = 0; i < brackets.size() - 1; i++)
	{
		slice[0] = brackets[i];
		slice[1] = brackets[i + 1];

		if (!strcmp(slice, "))") || !strcmp(slice, "()")) { ++acc; }
		else if (!strcmp(slice, ")(")) {
			if(acc2 == 0) {
				acc2 = acc;
			}
			else
			{
				acc2 *= acc;
			}
			acc = 0;
		}
	}	
	acc2 += acc;
	cout << acc << '\n';*/

	return 0;
}