This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const LL MOD = 1000000007;
LL check2(string s){
	vector<int> psums(1,0);
	for(int j = 0; j < s.size(); j++){
		if(s[j] == '('){
			psums.push_back(psums[psums.size() - 1] + 1);
		} else {
			psums.push_back(psums[psums.size() - 1] - 1);			
		}
	}
	int laste = psums.size() - 1;
	while(laste > 0 && psums[laste - 1] >= psums[psums.size() - 1]){
		laste--;
	}
	int lasts = 0;
	while(lasts + 1 < psums.size() && psums[lasts + 1] >= psums[0]){
		lasts++;
	}
	int a = psums[psums.size() - 1] / 2;
	if(lasts == psums.size() - 1 && laste == 0){
		return 1;
	} else if(lasts == psums.size() - 1){
		int maxv = 0;
		for(int i = laste; i < psums.size(); i++){
			maxv = max(maxv, psums[i] - psums[psums.size() - 1]);
		}
		for(int i = laste; i >= 0; i--){
			if(psums[i] - psums[psums.size() - 1] <= maxv - a) return 1;
			if(psums[i] - psums[psums.size() - 1] > 2 * maxv) return 0;
		}
	} else if(laste == 0){
		int maxv = 0;
		for(int i = 0; i <= lasts; i++){
			maxv = max(maxv, psums[i]);
		}
		for(int i = lasts; i < psums.size(); i++){
			if(psums[i] <= maxv + a) return 1;
			if(psums[i] > 2 * maxv) return 0;
		}
	} else {
		int maxl = psums[0];
		int maxm = psums[lasts];
		int maxr = psums[psums.size() - 1];
		for(int i = 0; i <= lasts; i++){
			maxl = max(maxl, psums[i]);
		}
		for(int i = lasts; i <= laste; i++){
			maxm = max(maxm, psums[i]);
		}
		for(int i = laste; i < psums.size(); i++){
			maxr = max(maxr, psums[i]);
		}
		return (maxm <= 2 * maxl && maxm <= 2 * (maxr - a));
	}
	return 0;
}
LL cnt(string s, int idx){
	if(idx == s.size()){
		return check2(s);
	}
	if(s[idx] != 'x'){
		return cnt(s, idx + 1);
	}
	string s1 = s;
	string s2 = s;
	s1[idx] = '(';
	s2[idx] = ')';
	for(int z = idx + 1; z <= s.size(); z++){
		if(z == s.size() || s[z] == 'x'){
			return (cnt(s1, z) + cnt(s2, z)) % MOD;
		}
	}
}
int main(){
	int n;
	string s;
	cin >> n >> s;
	if(n % 2 == 1){
		cout << 0 << '\n';
		return 0;
	}
	cout << cnt(s, 0) << '\n';
}
Compilation message (stderr)
securitygate.cpp: In function 'LL check2(std::__cxx11::string)':
securitygate.cpp:8:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int j = 0; j < s.size(); j++){
                 ~~^~~~~~~~~~
securitygate.cpp:20:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while(lasts + 1 < psums.size() && psums[lasts + 1] >= psums[0]){
        ~~~~~~~~~~^~~~~~~~~~~~~~
securitygate.cpp:24:11: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if(lasts == psums.size() - 1 && laste == 0){
     ~~~~~~^~~~~~~~~~~~~~~~~~~
securitygate.cpp:26:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  } else if(lasts == psums.size() - 1){
            ~~~~~~^~~~~~~~~~~~~~~~~~~
securitygate.cpp:28:24: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i = laste; i < psums.size(); i++){
                      ~~^~~~~~~~~~~~~~
securitygate.cpp:40:24: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i = lasts; i < psums.size(); i++){
                      ~~^~~~~~~~~~~~~~
securitygate.cpp:54:24: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for(int i = laste; i < psums.size(); i++){
                      ~~^~~~~~~~~~~~~~
securitygate.cpp: In function 'LL cnt(std::__cxx11::string, int)':
securitygate.cpp:63:9: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if(idx == s.size()){
     ~~~~^~~~~~~~~~~
securitygate.cpp:73:25: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int z = idx + 1; z <= s.size(); z++){
                       ~~^~~~~~~~~~~
securitygate.cpp:74:8: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if(z == s.size() || s[z] == 'x'){
      ~~^~~~~~~~~~~
securitygate.cpp:78:1: warning: control reaches end of non-void function [-Wreturn-type]
 }
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