#include <bits/stdc++.h>
#include "scales.h"
template <class T> using Vec = std::vector<T>;
std::array<std::array<int, 6>, 720> perm;
std::array<std::array<int, 4>, 120> query;
std::array<std::array<int, 120>, 720> rsp;
std::map<Vec<int>, int> memo;
int find_next(const Vec<int>& cand) {
const auto itr = memo.find(cand);
if (itr != memo.end()) {
return itr -> second;
}
const int sz = (int) cand.size();
if (sz == 1) {
return memo[cand] = -2;
}
int nsz = 1;
while (nsz * 3 < sz) {
nsz *= 3;
}
for (int i = 0; i < 120; ++i) {
std::map<int, Vec<int>> next;
for (const int p : cand) {
next[rsp[i][p]].push_back(p);
}
bool ok = true;
for (const auto& p: next) {
if ((int) p.second.size() > nsz or find_next(p.second) == -1) {
ok = false;
break;
}
}
if (ok) {
return memo[cand] = i;
}
}
return memo[cand] = -1;
}
void init(int) {
std::array<int, 6> ord;
std::iota(ord.begin(), ord.end(), 1);
for (int i = 0; i < 720; ++i) {
perm[i] = ord;
std::next_permutation(ord.begin(), ord.end());
}
int idx = 0;
for (int i = 0; i < 6; ++i) {
for (int j = i + 1; j < 6; ++j) {
for (int k = j + 1; k < 6; ++k) {
for (int l = 0; l < 6; ++l) {
query[idx++] = {i, j, k, l};
}
}
}
}
for (int i = 0; i < 120; ++i) {
auto ord = query[i];
for (int p = 0; p < 720; ++p) {
std::sort(ord.begin(), ord.begin() + 3, [&](const int x, const int y) {
return perm[p][x] < perm[p][y];
});
bool done = false;
for (int k = 0; k < 3; ++k) {
if (query[i][k] == query[i][3]) {
rsp[i][p] = ord[k];
done = true;
}
}
if (!done) {
int idx = 0;
while (perm[p][ord[idx]] < perm[p][ord[3]]) {
idx += 1;
}
rsp[i][p] = (idx == 3 ? ord[0] : ord[idx]);
}
}
}
}
void orderCoins() {
Vec<int> cand(720);
std::iota(cand.begin(), cand.end(), 0);
while (cand.size() > 1) {
const auto i = find_next(cand);
const auto [a, b, c, d] = query[i];
Vec<int> next;
const auto e = [&] {
if (a == d) return getLightest(a + 1, b + 1, c + 1) - 1;
if (b == d) return getMedian(a + 1, b + 1, c + 1) - 1;
if (c == d) return getHeaviest(a + 1, b + 1, c + 1) - 1;
return getNextLightest(a + 1, b + 1, c + 1, d + 1) - 1;
}();
for (const auto p : cand) {
if (rsp[i][p] == e) {
next.push_back(p);
}
}
cand = std::move(next);
}
const int p = cand[0];
int W[6];
std::iota(W, W + 6, 0);
std::sort(W, W + 6, [&](const int x, const int y) {
return perm[p][x] < perm[p][y];
});
for (auto& x : W) {
x += 1;
}
answer(W);
}
