#include <bits/stdc++.h>
#include "perm.h"
using namespace std;
using ll = long long;
vector<int> construct_permutation(ll k) {
bool tr1 = false, tr2 = false;
int mn = 0, smn = 0, mx = -1;
vector<double> v;
for (int i = 59; i >= 0; i--) {
if (!tr1 && !((k >> i) & 1)) continue;
bool x = (k >> i) & 1;
if (!i) {
v.push_back(++mx);
if (x) v.push_back(--mn);
break;
}
bool y = (k >> (i - 1)) & 1;
if (!x && !y) {
v.push_back(++mx);
v.push_back(++mx);
if (!tr1) smn = 1;
}
else if (!x) {
v.push_back(++mx);
v.push_back(++mx);
smn = mn;
v.push_back(--mn);
tr2 = true;
}
else if (!y) {
if (tr1) {
v.push_back(++mx);
smn = mn;
v.push_back(--mn);
tr2 = true;
}
v.push_back(++mx);
}
else {
if (!tr1) {
v.push_back(++mx);
smn = 0;
v.push_back(--mn);
tr2 = true;
}
else if (!tr2) {
v.push_back(++mx);
v.push_back(++mx);
v.push_back(mn + 0.5);
smn = mn;
v.push_back(--mn);
tr2 = true;
}
else {
v.push_back(++mx);
v.push_back(++mx);
v.push_back(smn + 0.0005 / (int)v.size());
}
}
i--;
tr1 = true;
}
int x = 0;
map<double, int> m;
for (auto i : v) {
m[i] = 1;
}
for (auto &i : m) {
i.second = x++;
}
vector<int> ans;
for (auto i : v) {
ans.push_back(m[i]);
}
return ans;
}
