#include "perm.h"
#include<bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define int long long
#define vi vector<signed>
#define vvi vector<vector<int>>
#define pii pair<int, int>
#define vpii vector<pair<int, int>>
#define vc vector<char>
#define vb vector<bool>
#define mii map<int,int>
#define f0r(i,n) for(int i=0;i<n;i++)
#define FOR(i,k,n) for(int i=k;i<n;i++)
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define in(a) int a; cin>>a
#define in2(a,b) int a,b; cin>>a>>b
#define in3(a,b,c) int a,b,c; cin>>a>>b>>c
#define in4(a,b,c,d) int a,b,c,d; cin>>a>>b>>c>>d
#define vin(v,n); vi v(n); f0r(i,n){cin>>v[i];}
#define out(a) cout<<a<<'\n'
#define out2(a,b) cout<<a<<' '<<b<<'\n'
#define out3(a,b,c) cout<<a<<' '<<b<<' '<<c<<'\n'
#define out4(a,b,c,d) cout<<a<<' '<<b<<' '<<c<<' '<<d<<'\n'
#define pout(a) cout<<a.first<<' '<<a.second<<'\n'
#define vout(v) for(auto u : v){cout<<u<<' ';} cout<<'\n'
#define dout(a) cout<<a<<' '<<#a<<'\n'
#define dout2(a,b) cout<<a<<' '<<#a<<' '<<b<<' '<<#b<<'\n'
#define yn(x); if(x){cout<<"YES"<<'\n';}else{cout<<"NO"<<'\n';}
const int leg = 1e9 + 7;
const int mod = 998244353;
using namespace std;
vi solve(int x, int dep){
if(x==2)return {0};
if(x==3)return {1,0};
vi d;
if(x%2==0){
vi tmp = solve(x/2,dep); tmp.pb(tmp.size()); d = tmp;
}
else if(x%2==1){
vi tmp = solve(x/2,dep); f0r(i,tmp.size())tmp[i]++; tmp.pb(tmp.size()+1); tmp.pb(0); d = tmp;
}
if(dep >= 10)return d;
vi e;
if(x % 3 == 0){
vi tmp = solve(x/3,dep+1); int s = tmp.size(); tmp.pb(s + 1); tmp.pb(s); e = tmp;
if(e.size() < d.size())return e; return d;
}
else return d;
}
std::vector<signed> construct_permutation(long long k)
{
vi ans = solve(k,0); return ans;
}
