#include "scales.h"
#include "bits/stdc++.h"
using namespace std;
#define ALL(x) (x.begin()), (x.end())
#define RALL(x) (x.rbegin()), (x.rend())
#define SZ(x) ((int)x.size())
#define fi first
#define se second
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef array<int, 5> arr5;
vvi perm;
vector<array<int, 6>> permPos(720);
int pow3[7];
void init(int T) {
pow3[0] = 1;
for (int i = 1; i < 7; i++) pow3[i] = pow3[i-1]*3;
vi p = {0, 1, 2, 3, 4, 5};
do { perm.push_back(p); } while(next_permutation(ALL(p)));
for (int i = 0; i < 720; i++) {
for (int j = 0; j < 6; j++) {
permPos[i][perm[i][j]] = j;
}
}
}
vvi split(vi &alive, arr5 q) {
auto [op, a, b, c, d] = q;
vvi ret(3);
for (int p : alive) {
vector<pii> v = {
{permPos[p][a], a},
{permPos[p][b], b},
{permPos[p][c], c}
};
sort(ALL(v));
int idx = 0;
if (op == 0) idx = (v[0].se == a) ? 0 : ((v[0].se == b) ? 1 : 2);
if (op == 1) idx = (v[1].se == a) ? 0 : ((v[1].se == b) ? 1 : 2);
if (op == 2) idx = (v[2].se == a) ? 0 : ((v[2].se == b) ? 1 : 2);
if (op == 3) {
int posa = permPos[p][a];
int posb = permPos[p][b];
int posc = permPos[p][c];
int posd = permPos[p][d];
vector<pii> v2;
if (posa > posd) v2.push_back({posa, a});
if (posb > posd) v2.push_back({posb, b});
if (posc > posd) v2.push_back({posc, c});
sort(ALL(v2));
if (SZ(v2)) idx = (v2[0].se == a) ? 0 : ((v2[0].se == b) ? 1 : 2);
else idx = (v[0].se == a) ? 0 : ((v[0].se == b) ? 1 : 2);
}
ret[idx].push_back(p);
}
return ret;
}
map<vi, arr5> dp;
arr5 solve(vi alive, int depth) {
if (dp.find(alive) != dp.end()) return dp[alive];
if (depth == 0) return (alive.size() <= 1) ? arr5{0} : arr5{-1};
if (SZ(alive) > pow3[depth]) return {-1};
vector<pair<int, arr5>> possible;
for (int op = 0; op < 4; op++) {
for (int a = 0; a < 6; a++) {
for (int b = a+1; b < 6; b++) {
for (int c = b+1; c < 6; c++) {
if (op < 3) {
int mx = 0;
vvi sp = split(alive, {op, a, b, c, -1});
for (int i = 0; i < 3; i++) mx = max(mx, SZ(sp[i]));
if (mx <= pow3[depth-1]) possible.push_back({mx, {op, a, b, c, -1}});
}
else {
for (int d = 0; d < 6; d++) if (d != a && d != b && d != c) {
int mx = 0;
vvi sp = split(alive, {op, a, b, c, d});
for (int i = 0; i < 3; i++) mx = max(mx, SZ(sp[i]));
if (mx <= pow3[depth-1]) possible.push_back({mx, {op, a, b, c, d}});
}
}
}
}
}
}
sort(ALL(possible));
for (auto [mx, q] : possible) {
vvi sp = split(alive, q);
bool ok = 1;
for (int i = 0; i < 3; i++) {
if (solve(sp[i], depth-1)[0] == -1) {
ok = 0;
break;
}
}
if (ok) return dp[alive] = q;
}
return {-1};
}
void orderCoins() {
vi alive(720);
for (int i = 0; i < 720; i++) alive[i] = i;
solve(alive, 6);
int depth = 6;
while (SZ(alive) > 1) {
arr5 q = solve(alive, depth);
auto [op, a, b, c, d] = q;
a++, b++, c++, d++;
int res = 0;
if (op == 0) res = getLightest(a, b, c);
if (op == 1) res = getMedian(a, b, c);
if (op == 2) res = getHeaviest(a, b, c);
if (op == 3) res = getNextLightest(a, b, c, d);
vvi sp = split(alive, q);
res = (res == a) ? 0 : ((res == b) ? 1 : 2);
alive = sp[res];
depth--;
}
int ans[6] = {0};
for (int i = 0; i < 6; i++) ans[i] = perm[alive[0]][i]+1;
//for (int i = 0; i < 6; i++) cout << ans[i] << " "; cout << endl;
answer(ans);
}
