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//
// ~oisín~ C++ Template
//
#include <bits/stdc++.h>
#include "cave.h"
#define MX_N 5001
#define mp make_pair
#define mod7 1000000007
#define modpi 314159
#define PI 3.141592653589793238
#define pb push_back
#define FastIO ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define All(a) a.begin(),a.end()
#define fi first
#define se second
#define ll long long int
#define ull unsigned long long int
int kx[8] = {+2, +2, -2, -2, +1, +1, -1, -1};
int ky[8] = {+1, -1, +1, -1, +2, -2, +2, -2};
int d9x[9] = {+1, +1, +1, +0, +0, +0, -1, -1, -1};
int d9y[9] = {+1, +0, -1, +1, +0, -1, +1, +0, -1};
int dx4[4] = {+0, +0, +1, -1};
int dy4[4] = {+1, -1, +0, +0};
ll gcd(ull a, ull b){
return (a==0)?b:gcd(b%a,a);
}
ll lcm(ull a, ull b){
return a*(b/gcd(a,b));
}
const long long INF = 1e18;
using namespace std;
//int p[MX_N];
//int o[MX_N];
int tryCombination(int S[]);
//int tryCombination(vector<int> S){
// int n = S.size();
// cout << "Trying this combination\n";
// for(int i=0;i<n;++i){
// cout << S[i] << ' ';
// }
// cout << endl;
// bool door[n];
// for(int i=0;i<n;++i){
// door[p[i]] = (S[i] == o[p[i]]);
// }
// for(int i=0;i<n;++i){
// if(!door[i]){
// cout << "It reaches all the way up to door " << i << "!\n";
// return i;
// }
// }
// cout << "It reaches all the way through!\n";
// return -1;
//}
void answer (int S[], int D[]);
//void answer (vector<int> S, vector<int> D){
// int n = S.size();
// for(int i=0;i<n;++i){
// cout << S[i] << " & " << D[i] << endl;
// }
// for(int i=0;i<n;++i){
// if(!(S[i] == o[D[i]] && D[i] == p[i])){
// cout << "WA\n";
// return;
// }
// }
// cout << "AC\n";
// return;
//}
void exploreCave(int N){
int k[N];
bool dk[N];
int pos[N];//correct orientation of lever i
memset(pos, -1, sizeof(pos));
memset(k, 0, sizeof(k));
for(int i=0;i<N;++i){
dk[i] = 1;
}
for(int root=0;root<N;++root){
int S[N];
for(int i=0;i<N;++i){
if(dk[i]){
S[i] = 1;
}else{
S[i] = pos[i];
}
}
int res = tryCombination(S);
bool O = (res > root || res == -1);
int lo=0, hi=N-1-root;
while(lo < hi){
int mid = (lo+hi) >> 1;
int cnt = 0;
for(int i=0;i<N;++i){
if(dk[i] == false){
continue;
}
if(cnt <= mid){
S[i] = O;
}else{
S[i] = !O;
}
++cnt;
}
res = tryCombination(S);
if(res > root || res == -1){
hi = mid;
}else{
lo = mid+1;
}
}
int cnt = 0;
for(int i=0;i<N;++i){
if(dk[i] == false){
continue;
}
if(cnt == lo){
k[i] = root;
pos[i] = O;
dk[i] = false;
break;
}
++cnt;
}
}
int S[N];
int D[N];
for(int i=0;i<N;++i){
S[i] = pos[i];
D[i] = k[i];
}
answer(S, D);
return;
}
//int main(){
// int n;
// cin >> n;
// cout << "Orientation:\n";
// for(int i=0;i<n;++i){
// cin >> o[i];
// }
// cout << "Permutation\n";
// for(int i=0;i<n;++i){
// cin >> p[i];
// }
// exploreCave(n);
// return 0;
//}
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