#include "bits/extc++.h"
using namespace std;
template <typename T>
void dbgh(const T& t) {
cerr << t << endl;
}
template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
cerr << t << " | ";
dbgh(u...);
}
#ifdef DEBUG
#define dbg(...) \
cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \
dbgh(__VA_ARGS__);
#else
#define dbg(...)
#define cerr \
if (false) \
cerr
#endif
#define endl "\n"
#define long int64_t
#define sz(x) int((x).size())
void add_element(string x);
bool check_element(string x);
void compile_set();
int n;
vector<int> ans;
void dfs1(int bit, const vector<int>& cur) {
if (sz(cur) == 1) {
return;
}
bool vis[n] {};
for (auto& a : cur) {
vis[a] = true;
}
vector<int> l, r;
for (auto& a : cur) {
if ((a >> bit) & 1) {
string s(n, '0');
for (int i = 0; i < n; i++) {
if (!vis[i]) {
s[i] = '1';
}
}
s[a] = '1';
add_element(s);
l.push_back(a);
} else {
r.push_back(a);
}
}
dfs1(bit + 1, l);
dfs1(bit + 1, r);
}
void dfs2(int bit, const vector<int>& cur) {
if (sz(cur) == 1) {
return;
}
bool vis[n] {};
for (auto& a : cur) {
vis[a] = true;
}
vector<int> l, r;
for (auto& a : cur) {
string s(n, '0');
for (int i = 0; i < n; i++) {
if (!vis[i]) {
s[i] = '1';
}
}
s[a] = '1';
if (check_element(s)) {
ans[a] |= 1 << bit;
l.push_back(a);
} else {
r.push_back(a);
}
}
dfs2(bit + 1, l);
dfs2(bit + 1, r);
}
vector<int> restore_permutation(int _n, int, int) {
n = _n;
ans.resize(n);
vector<int> arr(n);
iota(begin(arr), end(arr), 0);
dfs1(0, arr);
compile_set();
dfs2(0, arr);
return ans;
}
