#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
edi
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "scales.h"
ll n = 6;
vector<ll> pow3(15);
vector<array<ll,4>> ops;
map< tuple< vector<vector<ll>>, ll, ll>, bool > mp;
bool go(vector<vector<ll>> &a, ll ind, ll m){
// can make m more guesses
if(m < 0) return false;
if(sz(a) > pow3[m]) return false;
if(m == 0) return true;
if(ind >= sz(ops)) return false;
if(mp.count({a,ind,m})) return mp[{a,ind,m}];
// do op
auto [i,j,k,t] = ops[ind];
vector<vector<ll>> v1,v2,v3;
trav(v,a){
if(t == 0){
if(v[i] < v[j] and v[i] < v[k]){
v1.pb(v);
}
else if(v[j] < v[i] and v[j] < v[k]){
v2.pb(v);
}
else{
v3.pb(v);
}
}
else if(t == 1){
if(v[i] > min(v[j],v[k]) and v[i] < max(v[j],v[k])){
v1.pb(v);
}
else if(v[j] > min(v[i],v[k]) and v[j] < max(v[i],v[k])){
v2.pb(v);
}
else{
v3.pb(v);
}
}
else if(t == 2){
if(v[i] > v[j] and v[i] > v[k]){
v1.pb(v);
}
else if(v[j] > v[i] and v[j] > v[k]){
v2.pb(v);
}
else{
v3.pb(v);
}
}
}
bool ans = go(v1,ind+1,m-1)&go(v2,ind+1,m-1)&go(v3,ind+1,m-1);
if(ans) return true;
// skip
ans = go(a,ind+1,m);
return mp[{a,ind,m}] = ans;
}
vector<vector<ll>> adj;
vector<vector<vector<ll>>> here;
vector<ll> op;
void init(int T) {
pow3[0] = 1;
rep1(i,10) pow3[i] = pow3[i-1]*3;
rep(i,n){
for(int j = i+1; j < n; ++j){
for(int k = j+1; k < n; ++k){
rep(t,3){
ops.pb({i,j,k,t});
}
}
}
}
// mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937 rng(1);
shuffle(all(ops),rng);
vector<vector<ll>> perms;
vector<ll> a(n);
iota(all(a),1);
do{
perms.pb(a);
} while(next_permutation(all(a)));
bool ok = go(perms,0,7);
ll ptr = 0;
auto new_node = [&](vector<vector<ll>> v){
adj.pb(vector<ll>());
here.pb(v);
op.pb(0);
return ptr++;
};
queue<tuple< vector<vector<ll>>, ll, ll, ll>> q;
q.push({perms,0,7,new_node(perms)});
while(!q.empty()){
auto [a,ind,m,u] = q.front();
q.pop();
if(sz(a) <= 1) conts;
assert(m >= 1);
bool ok = false;
for(int opi = ind; opi < sz(ops); ++opi){
auto [i,j,k,t] = ops[opi];
vector<vector<ll>> v1,v2,v3;
trav(v,a){
if(t == 0){
if(v[i] < v[j] and v[i] < v[k]){
v1.pb(v);
}
else if(v[j] < v[i] and v[j] < v[k]){
v2.pb(v);
}
else{
v3.pb(v);
}
}
else if(t == 1){
if(v[i] > min(v[j],v[k]) and v[i] < max(v[j],v[k])){
v1.pb(v);
}
else if(v[j] > min(v[i],v[k]) and v[j] < max(v[i],v[k])){
v2.pb(v);
}
else{
v3.pb(v);
}
}
else if(t == 2){
if(v[i] > v[j] and v[i] > v[k]){
v1.pb(v);
}
else if(v[j] > v[i] and v[j] > v[k]){
v2.pb(v);
}
else{
v3.pb(v);
}
}
}
bool res = go(v1,opi+1,m-1)&go(v2,opi+1,m-1)&go(v3,opi+1,m-1);
if(res){
ok = true;
op[u] = opi;
for(auto v : {v1,v2,v3}){
ll x = new_node(v);
adj[u].pb(x);
q.push({v,opi+1,m-1,x});
}
break;
}
}
}
}
void found(vector<ll> a){
int ans[6];
rep(i,6) ans[a[i]-1] = i+1;
answer(ans);
}
void orderCoins() {
ll u = 0;
while(true){
auto &a = here[u];
if(sz(a) == 1){
found(a[0]);
return;
}
ll ind = op[u];
auto [i,j,k,t] = ops[ind];
i++, j++, k++;
ll res = 0;
if(t == 0){
res = getLightest(i,j,k);
}
else if(t == 1){
res = getMedian(i,j,k);
}
else if(t == 2){
res = getHeaviest(i,j,k);
}
else{
assert(0);
}
if(res == i){
u = adj[u][0];
}
else if(res == j){
u = adj[u][1];
}
else{
u = adj[u][2];
}
}
}
