#include "cave.h"
#include <bits/stdc++.h>
using namespace std;
#define name "cave"
#define MAXN 100005
#define pb push_back
#define pf push_front
#define ll long long
#define ii pair<int, int>
#define fs first
#define sc second
#define ill pair<int, ll>
#define lli pair<ll, int>
#define llll pair<ll, ll>
#define all(v) v.begin(),v.end()
#define uni(v) v.erase(unique(all(v)),v.end())
#define bit(n,i) (((n)>>(i))&1)
#define FOR(i,a,b) for (int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for (int i=(a),_b=(b); i>=_b; i--)
#define MASK(i) (1LL<<(i))
const int INF=1e9;
const int MOD=1e9+7;
void add(int &u, int v){
u+=v;
if (u>=MOD) u-=MOD;
}
void sub(int &u, int v){
u-=v;
if (u<0) u+=MOD;
}
void minimize(int &u, int v){
u=min(u,v);
}
void maximize(int &u, int v){
u=max(u,v);
}
long long Rand(long long l, long long r){
ll tmp=0;
FOR(i,1,4) tmp=((tmp<<15)^(((1<<15)-1)&rand()));
return l+tmp%(r-l+1);
}
int S[MAXN],D[MAXN];
bool mark[MAXN];
int dnc(int l, int r, int id, int color){
if (l==r) return l;
int mid=(l+r)/2;
FOR(i,l,mid){
if (!mark[i]){
S[i]=color;
}
}
int x=tryCombination(S);
FOR(i,l,mid) if (!mark[i]) S[i]^=1;
if (x!=id) return dnc(l,mid,id,color);
return dnc(mid+1,r,id,color);
}
void exploreCave(int N){
FOR(i,0,N-1) S[i]=0;
FOR(i,0,N-1){
int x=tryCombination(S);
int u=-1;
if (x!=i){
FOR(j,0,N-1) if (!mark[j]){
u=S[j];
S[j]^=1;
}
}
else{
FOR(j,0,N-1){
if (!mark[j]) u=S[j]^1;
}
}
int y=dnc(0,N-1,i,u);
mark[y]=1;
S[y]^=1;
D[y]=i;
}
answer(S,D);
}
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