#include <vector>
#include "messy.h" //"grader.cpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
#define REP(i,n) for (int i = 0; i < n; i++)
#define all(x) (x).begin(), (x).end()
#define trav(x) for (auto &a : x)
#define D(x) //cerr << #x << ": " << x << endl;
int n;
vi perm; // from where?
vi to;
bool check(vector<char> vc) {
return check_element(string(all(vc)));
}
void add(vector<char> vc) {
add_element(string(all(vc)));
}
void prep_learn(int am) {
vector<char> st(n, '0');
REP(i,am) {
st[i] = '1';
add(st);
}
}
void prep_power(int pw) {
vector<char> st(n, '0');
REP(i,4) {
if (i == 0) st[i] = '0';
else if (i == 1) st[i] = ((pw+1)&4) ? '1' : '0';
else if (i == 2) st[i] = ((pw+1)&2) ? '1' : '0';
else if (i == 3) st[i] = ((pw+1)&1) ? '1' : '0';
}
REP(i,n) {
if (i < 4) continue;
st[i] = (i&(1<<pw)) ? '1' : '0';
if (st[i] == '1') add(st);
st[i] = '0';
}
}
void prep_powers() {
REP(i, 5) prep_power(i);
}
void learn_brute(int am) {
vector<char> st(n, '0');
REP(i,am) {
REP(j,n) {
if (st[j] == '1') continue;
st[j] = '1';
if (check(st)) {
to[i] = j;
perm[j] = i;
break;
} else st[j] = '0';
}
D(to[i]);
if (to[i] == -1) D(i);
}
}
bool ask_pow(int pw, int tar) {
vector<char> st(n, '0');
REP(i,4) {
if (i == 0) st[to[i]] = '0';
else if (i == 1) st[to[i]] = ((pw+1)&4) ? '1' : '0';
else if (i == 2) st[to[i]] = ((pw+1)&2) ? '1' : '0';
else if (i == 3) st[to[i]] = ((pw+1)&1) ? '1' : '0';
}
assert(tar != to[0]);
assert(tar != to[1]);
assert(tar != to[2]);
assert(tar != to[3]);
st[tar] = '1';
return check(st);
}
void learn_powers() {
REP(i, n) {
if (perm[i] != -1) continue;
int ind = 0;
REP(pw, 5) {
if (ask_pow(pw, i)) ind += 1<<pw;
}
perm[i] = ind;
}
}
std::vector<int> restore_permutation(int n_, int w, int r) {
n = n_;
perm = vi(n,-1); to = vi(n,-1);
prep_learn(4);
prep_powers();
compile_set();
learn_brute(4);
learn_powers();
return perm;
}
