#include "scales.h"
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define sz(a) (int)((a).size())
#define ff first
#define ss second
constexpr int maxn = 2020;
vector<vector<int>> permutacoes;
vector<pair<int, vector<int>>> operacoes;
int fim[maxn], go[maxn];
bool solve(int pos, int size, vector<int> possible) {
if(sz(possible) <= 1) {
if(sz(possible) == 1) {
fim[pos] = 1;
go[pos] = possible[0];
}
return true;
}
for(int g = 0; g < sz(operacoes); g++) {
auto op = operacoes[g];
bool ok = 1;
vector<int> ans[3];
for(int p : possible) {
int x = permutacoes[p][op.ss[0]];
int y = permutacoes[p][op.ss[1]];
int z = permutacoes[p][op.ss[2]];
int decode[6], val[3] = {x, y, z};
sort(val, val+3);
decode[x] = 0;
decode[y] = 1;
decode[z] = 2;
if(op.ff == 1) ans[decode[val[0]]].pb(p);
else if(op.ff == 2) ans[decode[val[1]]].pb(p);
else if(op.ff == 3) ans[decode[val[2]]].pb(p);
else {
int w = permutacoes[p][op.ss[3]];
if(w > val[2] || w < val[0]) ans[decode[val[0]]].pb(p);
else if(w < val[1]) ans[decode[val[1]]].pb(p);
else ans[decode[val[2]]].pb(p);
}
}
if(max({sz(ans[0]), sz(ans[1]), sz(ans[2])}) > size) continue;
for(int i : {0, 1, 2})
ok &= solve(3*pos+i, size/3, ans[i]);
if(ok) {
go[pos] = g;
return true;
}
}
return false;
}
void init(int T) {
++T;
vector<int> vec(6);
iota(all(vec), 0);
do {
permutacoes.pb(vec);
} while(next_permutation(all(vec)));
vector<int> list(720);
iota(all(list), 0);
for(int mask = 0; mask < (1<<6); mask++) {
if(__builtin_popcount(mask) != 3) continue;
vector<int> ligado;
for(int i = 0; i < 6; i++)
if(mask&(1<<i))
ligado.pb(i);
for(int i : {1, 2, 3})
operacoes.pb({i, ligado});
for(int i = 0; i < 6; i++) {
if(mask&(1<<i)) continue;
ligado.pb(i);
operacoes.pb({4, ligado});
ligado.pop_back();
}
}
solve(1, 243, list);
}
int get(int pos) {
if(fim[pos]) return go[pos];
auto op = operacoes[go[pos]];
int ans;
if(op.ff == 1) ans = getLightest(op.ss[0]+1, op.ss[1]+1, op.ss[2]+1);
else if(op.ff == 2) ans = getMedian(op.ss[0]+1, op.ss[1]+1, op.ss[2]+1);
else if(op.ff == 3) ans = getHeaviest(op.ss[0]+1, op.ss[1]+1, op.ss[2]+1);
else ans = getNextLightest(op.ss[0]+1, op.ss[1]+1, op.ss[2]+1, op.ss[3]+1);
if(ans == op.ss[0]+1) return get(3*pos);
if(ans == op.ss[1]+1) return get(3*pos+1);
return get(3*pos+2);
}
void orderCoins() {
int pos = get(1), W[6];
for(int i = 0; i < 6; i++)
W[permutacoes[pos][i]] = i+1;
answer(W);
}
