#include <bits/stdc++.h>
#include "scales.h"
using namespace std;
constexpr int N = 6, M = 720, P[]{1, 3, 9, 27, 81, 243, 729};
map<vector<int>, array<int, 4>> compare;
vector<int> perm[M], inv[M];
int ans[N];
void sort(vector<int> &p, int &i, int &j, int &k) {
if (p[i] > p[j]) {
swap(i, j);
}
if (p[i] > p[k]) {
swap(i, k);
}
if (p[j] > p[k]) {
swap(j, k);
}
}
int heaviest(vector<int> &p, int i, int j, int k) {
sort(p, i, j, k);
return k;
}
int median(vector<int> &p, int i, int j, int k) {
sort(p, i, j, k);
return j;
}
int lightest(vector<int> &p, int i, int j, int k) {
sort(p, i, j, k);
return i;
}
int next(vector<int> &p, int i, int j, int k, int l) {
sort(p, i, j, k);
if (p[l] < p[i] || p[l] > p[k]) {
return i;
} else if (p[l] < p[j]) {
return j;
} else {
return k;
}
}
bool solve(vector<int> mask, int remain) {
if (mask.size() <= 1 || compare.count(mask)) {
return true;
} else if (mask.size() > P[remain]) {
return false;
}
for (int i = 0; i < N - 2; ++i) {
for (int j = i + 1; j < N - 1; ++j) {
for (int k = j + 1; k < N; ++k) {
vector<int> one, two, three;
for (int p: mask) {
int x = heaviest(inv[p], i, j, k);
(x == i ? one : (x == j ? two : three)).push_back(p);
}
if (solve(one, remain - 1) && solve(two, remain - 1) && solve(three, remain - 1)) {
compare[mask] = {i, j, k, -1};
return true;
}
one = two = three = {};
for (int p: mask) {
int x = median(inv[p], i, j, k);
(x == i ? one : (x == j ? two : three)).push_back(p);
}
if (solve(one, remain - 1) && solve(two, remain - 1) && solve(three, remain - 1)) {
compare[mask] = {i, j, k, -2};
return true;
}
one = two = three = {};
for (int p: mask) {
int x = lightest(inv[p], i, j, k);
(x == i ? one : (x == j ? two : three)).push_back(p);
}
if (solve(one, remain - 1) && solve(two, remain - 1) && solve(three, remain - 1)) {
compare[mask] = {i, j, k, -3};
return true;
}
for (int l = 0; l < N; ++l) {
if (i != l && j != l && k != l) {
one = two = three = {};
for (int p: mask) {
int x = next(inv[p], i, j, k, l);
(x == i ? one : (x == j ? two : three)).push_back(p);
}
if (solve(one, remain - 1) && solve(two, remain - 1) && solve(three, remain - 1)) {
compare[mask] = {i, j, k, l};
return true;
}
}
}
}
}
}
return false;
}
void init(int T) {
vector<int> p(N);
iota(p.begin(), p.end(), 0);
for (int i = 0; i < M; ++i) {
inv[i].resize(N);
for (int k = 0; k < N; ++k) {
inv[i][p[k]] = k;
}
perm[i] = p;
next_permutation(p.begin(), p.end());
}
vector<int> mask(M);
iota(mask.begin(), mask.end(), 0);
assert(solve(mask, N));
}
void orderCoins() {
vector<int> mask(M);
iota(mask.begin(), mask.end(), 0);
while (mask.size() > 1) {
assert(compare.count(mask));
auto [i, j, k, l] = compare[mask];
vector<int> one, two, three;
int y;
if (l == -1) {
for (int p: mask) {
int x = heaviest(inv[p], i, j, k);
(x == i ? one : x == j ? two : three).push_back(p);
}
y = getHeaviest(i + 1, j + 1, k + 1) - 1;
} else if (l == -2) {
for (int p: mask) {
int x = median(inv[p], i, j, k);
(x == i ? one : x == j ? two : three).push_back(p);
}
y = getMedian(i + 1, j + 1, k + 1) - 1;
} else if (l == -3) {
for (int p: mask) {
int x = lightest(inv[p], i, j, k);
(x == i ? one : x == j ? two : three).push_back(p);
}
y = getLightest(i + 1, j + 1, k + 1) - 1;
} else {
for (int p: mask) {
int x = next(inv[p], i, j, k, l);
(x == i ? one : x == j ? two : three).push_back(p);
}
y = getNextLightest(i + 1, j + 1, k + 1, l + 1) - 1;
}
mask = (y == i ? one : (y == j ? two : three));
}
for (int i = 0; i < N; ++i) {
ans[i] = perm[mask[0]][i] + 1;
}
answer(ans);
}
