#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>> perm;
vector<pair<int,vector<int>>> operacoes;
int cool[maxn], ended[maxn], pot[7];
bool solve(int pos, int steps, vector<int> possible) {
if(sz(possible) <= 1) {
if(sz(possible) == 1)
cool[pos] = possible[0], ended[pos] = 1;
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 = perm[p][op.ss[0]];
int y = perm[p][op.ss[1]];
int z = perm[p][op.ss[2]];
int val[] = {x, y, z}, decode[6];
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 = perm[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])}) > pot[steps-1])
continue;
for(int i = 0; i < 3; i++) {
ok &= solve(pos*3 + i, steps-1, ans[i]);
if(!ok) continue;
}
if(ok) {
cool[pos] = g;
return true;
}
}
return false;
}
void init(int T) {
++T;
pot[0] = 1;
for(int i = 1; i < 7; i++)
pot[i] = 3*pot[i-1];
vector<int> pos(6);
iota(pos.begin(), pos.end(), 0);
do {
perm.pb(pos);
} while(next_permutation(pos.begin(), pos.end()));
for(int mask = 0; mask < (1 << 6); mask++) {
if(__builtin_popcount(mask) != 3) continue;
vector<int> ligados;
for(int i = 0; i < 6; i++)
if(mask&(1<<i)) ligados.pb(i);
for(int i = 1; i < 4; i++)
operacoes.pb({i, ligados});
for(int i = 0; i < 6; i++) {
if(!(mask&(1<<i))) {
ligados.pb(i);
operacoes.pb({4, ligados});
ligados.pop_back();
}
}
}
vector<int> lista(720);
iota(all(lista), 0);
solve(1, 6, lista);
}
int get(int pos) {
if(ended[pos]) return cool[pos];
auto op = operacoes[cool[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);
for(int i = 0; i < 3; i++)
if(op.ss[i]+1 == ans) return get(pos*3 + i);
assert(0);
return -1;
}
void orderCoins() {
int pos = get(1);
int W[6];
for(int i = 0; i < 6; i++)
W[i] = perm[pos][i]+1;
answer(W);
}
