#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include "cave.h"
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef pair<int, pi> pii;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
#define fax(i, a) for (int i = 0; i < (a); i++)
#define f0x(i, a, b) for (int i = (a); i < (b); i++)
#define f0xd(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define faxd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)
#define memeset memset
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rsz resize
template<class T> void ckmin(T &a, T b) { a = min(a, b); }
template<class T> void ckmax(T &a, T b) { a = max(a, b); }
template <class T, int ...Ns> struct BIT {
T val = 0;
void upd(T v) { val += v; }
T query() { return val; }
};
template <class T, int N, int... Ns> struct BIT<T, N, Ns...> {
BIT<T,Ns...> bit[N + 1];
template<typename... Args> void upd(int pos, Args... args) {
for (; pos <= N; pos += (pos&-pos)) bit[pos].upd(args...);
}
template<typename... Args> T sum(int r, Args... args) {
T res = 0; for (; r; r -= (r&-r)) res += bit[r].query(args...);
return res;
}
template<typename... Args> T query(int l, int r, Args... args) {
return sum(r,args...)-sum(l-1,args...);
}
};
namespace input {
template<class T> void re(complex<T>& x);
template<class T1, class T2> void re(pair<T1,T2>& p);
template<class T> void re(vector<T>& a);
template<class T, size_t SZ> void re(array<T,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(double& x) { string t; re(t); x = stod(t); }
void re(ld& x) { string t; re(t); x = stold(t); }
template<class T, class... Ts> void re(T& t, Ts&... ts) {
re(t); re(ts...);
}
template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
template<class T> void re(vector<T>& a) { fax(i,sz(a)) re(a[i]); }
template<class T, size_t SZ> void re(array<T,SZ>& a) { fax(i,SZ) re(a[i]); }
}
using namespace input;
namespace output {
void pr(int x) { cout << x; }
void pr(long x) { cout << x; }
void pr(ll x) { cout << x; }
void pr(unsigned x) { cout << x; }
void pr(unsigned long x) { cout << x; }
void pr(unsigned long long x) { cout << x; }
void pr(float x) { cout << x; }
void pr(double x) { cout << x; }
void pr(ld x) { cout << x; }
void pr(char x) { cout << x; }
void pr(const char* x) { cout << x; }
void pr(const string& x) { cout << x; }
void pr(bool x) { pr(x ? "true" : "false"); }
template<class T1, class T2> void pr(const pair<T1,T2>& x);
template<class T> void pr(const T& x);
template<class T, class... Ts> void pr(const T& t, const Ts&... ts) {
pr(t); pr(ts...);
}
template<class T1, class T2> void pr(const pair<T1,T2>& x) {
pr("{",x.f,", ",x.s,"}");
}
template<class T> void pr(const T& x) {
pr("{"); // const iterator needed for vector<bool>
bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0;
pr("}");
}
void ps() { pr("\n"); } // print w/ spaces
template<class T, class... Ts> void ps(const T& t, const Ts&... ts) {
pr(t); if (sizeof...(ts)) pr(" "); ps(ts...);
}
void pc() { pr("]\n"); } // debug w/ commas
template<class T, class... Ts> void pc(const T& t, const Ts&... ts) {
pr(t); if (sizeof...(ts)) pr(", "); pc(ts...);
}
#define dbg(x...) pr("[",#x,"] = ["), pc(x);
}
using namespace output;
namespace io {
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void setIO(string s = "") {
ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
}
using namespace io;
mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());
const int MOD = 1000000007; // 998244353
const ll INF = 1e18;
const int MX = 200005;
const ld PI = 4*atan((ld)1);
map<int,int> conn; int p[MX];
void exploreCave(int N){
fax(i,N){
p[i] = -1;
}
fax(i,N){
int inp[N];
fax(j,N){
if(p[j] == -1){
inp[j] = 1;
}
else{
inp[j] = p[j];
}
}
bool c = (tryCombination(inp) != i);
int lo = 0; int hi = N-1; int pos = -1;
while(lo <= hi){
int mid = lo + (hi-lo)/2;
bool works = false;
int tri[N];
fax(j,mid+1){
tri[j] = (p[j] < 0 ? !c : p[j]);
}
f0x(j,mid+1,N){
tri[j] = (p[j] < 0 ? c : p[j]);
}
int qry = tryCombination(tri);
works = (qry == i);
if(works){
hi = mid-1;
pos = mid;
}
else{
lo = mid+1;
}
}
conn[pos] = i;
p[pos] = c;
}
int ret[2][N];
fax(i,N){
ret[0][i] = conn[i];
ret[1][i] = p[i];
}
answer(ret[1], ret[0]);
}
