#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;
set<int>three, five, minu, mint, minf; map<int,int>memo;
int solve(int x, int dep){
if(memo.count(x))return memo[x];
if(x==2){memo[x]=1;return 1;}
if(x==3){memo[x]=2;return 2;}
int d;
if(x%2==0){
int tmp = solve(x/2,dep); d = tmp + 1;
}
else if(x%2==1){
int tmp = solve(x/2,dep); d = tmp + 2;
}
if(dep >= 12){memo[x]=d; return d;}
int e = 1e9;
if(x % 3 == 0){
int tmp = solve(x/3,dep+1); e = tmp + 2;
}
int f = 1e9; if(x%5==0 && x >= 10){
int tmp = solve(x/5,dep+1); f = tmp + 3;
}
int g = 1e9; int tmp = solve(x-1, dep+1); g = tmp + 1;
int h = 1e9; tmp = solve(x-2, dep+1); h = tmp + 2;
int j = 1e9; if(x>=5)tmp = solve(x-3, dep+1), j = tmp + 3;
int mn = min({d,e,f,g,h,j}); if(mn==d){} else if(mn==e)three.insert(x); else if(mn==f)five.insert(x);
else if(mn==g)minu.insert(x); else if(mn==j)minf.insert(x); else mint.insert(x);
memo[x]=mn; return mn;
}
vi get(int x){
if(x==2)return {0}; if(x==3)return {1,0};
if(five.count(x)){
vi tmp = get(x/5); int s = tmp.size(); tmp.pb(s+2); tmp.pb(s); tmp.pb(s+1); return tmp;
}
if(three.count(x)){
vi tmp = get(x/3); int s = tmp.size(); tmp.pb(s+1); tmp.pb(s); return tmp;
}
if(minu.count(x)){
vi tmp = get(x-1); int s = tmp.size(); vi nxt; nxt.pb(s); for(auto u : tmp)nxt.pb(u); return nxt;
}
if(minf.count(x)){
vi tmp = get(x-3); int s = tmp.size(); vi nxt; nxt.pb(s); nxt.pb(s+1); for(auto u : tmp)nxt.pb(u); return nxt;
}
if(mint.count(x)){
vi tmp = get(x-2); int s = tmp.size(); vi nxt; nxt.pb(s+1); nxt.pb(s); for(auto u : tmp)nxt.pb(u); return nxt;
}
if(x%2==0){
vi tmp = get(x/2); tmp.pb(tmp.size()); return tmp;
}
else{
vi tmp = get(x/2); f0r(i,tmp.size())tmp[i]++; tmp.pb(tmp.size()+1); tmp.pb(0); return tmp;
}
}
std::vector<signed> construct_permutation(long long k)
{
solve(k,0); int cur = k; vi ans = get(k);
return ans;
}
