Balans infopro XI

#include <bits/stdc++.h>

using namespace std;

ifstream fin("balans2.in");
ofstream fout("balans2.out");

int main() {
    fin.sync_with_stdio(false);
    fout.sync_with_stdio(false);
    fin.tie(nullptr);
    fout.tie(nullptr);
    int N;
    string s;
    fin >> N >> s;
    bool found = false;
    for(int i = 0; i < N && !found; ++i)
        if(s[i] == 'P')
            found = true;
    if(!found) {
        bool wrong = false;
        int cnt = 0;
        for(int i = 0; i < N; ++i) {
            if(s[i] == '(')
                ++cnt;
            else
                --cnt;
            if(cnt == 0 && !wrong)
                fout << '1';
            else {
                fout << '0';
                if(cnt < 0)
                    wrong = true;
            }
        }
        return 0;
    }
    int cnt = 0;
    queue < int > Q, last;
    char correct = '1';
    for(int i = 0; i < N; ++i) {
        if(s[i] == '(' || s[i] == ')') {
            if(s[i] == '(')
                ++cnt;
            else
                --cnt;
            if(cnt != 0) {
                correct = '0';
                if(cnt < 0 && s[i] == ')') {
                    last.emplace(i);
                    cnt = 0;
                }
            }
            else {
                if(last.empty())
                    correct = '1';
                else
                    correct = '0';
            }
            Q.emplace(i);
        }
        else {
            int curr = Q.front();
            Q.pop();
            if(!last.empty() && last.front() == curr)
                last.pop();
            else {
                if(s[curr] == '(')
                    --cnt;
                else
                    ++cnt;
            }
            if(correct == '1')
                correct = '0';
            else {
                if(last.empty() && cnt == 0)
                    correct = '1';
                else
                    correct = '0';
            }
        }
        fout << correct;
    }
}