#include "bits/extc++.h"
using namespace std;
template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
cerr << t;
((cerr << " | " << u), ...);
cerr << endl;
}
#ifdef DEBUG
#define dbg(...) \
cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \
dbgh(__VA_ARGS__)
#else
#define dbg(...)
#define cerr \
if (false) \
cerr
#endif
using u64 = uint64_t;
#define endl "\n"
#define long int64_t
#define sz(x) int(std::size(x))
#ifdef __cplusplus
extern "C" {
#endif
void init(int T);
void orderCoins();
void answer(int W[]);
int getMedian(int A, int B, int C);
int getHeaviest(int A, int B, int C);
int getLightest(int A, int B, int C);
int getNextLightest(int A, int B, int C, int D);
#ifdef __cplusplus
}
#endif
struct G {
int q_median(int a, int b, int c) {
return getMedian(a + 1, b + 1, c + 1) - 1;
}
int q_heaviest(int a, int b, int c) {
return getHeaviest(a + 1, b + 1, c + 1) - 1;
}
int q_lightest(int a, int b, int c) {
return getLightest(a + 1, b + 1, c + 1) - 1;
}
int q_next_lightest(int a, int b, int c, int d) {
return getNextLightest(a + 1, b + 1, c + 1, d + 1) - 1;
}
} G;
template <typename Cb>
struct Cmp {
Cb cb;
Cmp(Cb cb) : cb(cb) {}
template <typename T>
bool operator()(const T& a, const T& b) const {
return cb(a) < cb(b);
}
};
template <typename T>
ostream& operator<<(ostream& out, const vector<T>& arr) {
out << "[";
for (int i = 0; i < sz(arr); i++) {
if (i) {
out << ", ";
}
out << arr[i];
}
return out << "]";
}
vector<vector<int>> perms;
array<int, 3> sorted(int o, int a, int b, int c) {
array<int, 3> ans {a, b, c};
sort(begin(ans), end(ans), Cmp([&](int u) -> int { return perms[o][u]; }));
return ans;
}
int q_median(int o, int a, int b, int c) {
return sorted(o, a, b, c)[1];
}
int q_lightest(int o, int a, int b, int c) {
return sorted(o, a, b, c)[0];
}
int q_heaviest(int o, int a, int b, int c) {
return sorted(o, a, b, c)[2];
}
int q_next_lightest(int o, int a, int b, int c, int d) {
Cmp cmp([&](int u) -> int { return perms[o][u]; });
vector<int> gt;
for (auto& i : {a, b, c}) {
if (perms[o][i] > perms[o][d]) {
gt.push_back(i);
}
}
if (sz(gt)) {
return *min_element(begin(gt), end(gt), cmp);
}
return q_lightest(o, a, b, c);
}
u64 r_vals[720];
int p_mul[720][720];
map<u64, int> memo;
int dp(const vector<int>& arr) {
if (sz(arr) <= 1) {
return 0;
}
int p3 = 1, log3 = 0;
while (p3 < sz(arr)) {
p3 *= 3;
log3++;
}
u64 k_hash = 0;
for (auto& a : arr) {
k_hash += r_vals[a];
}
auto [it, inserted] = memo.emplace(k_hash, 0);
int& ans = it->second;
if (!inserted) {
return ans;
}
ans = 1e9;
for (int i = 0; i < 6; i++) {
for (int j = i + 1; j < 6; j++) {
for (int k = j + 1; k < 6; k++) {
auto go = [&](auto cb) -> void {
if (ans == log3) {
return;
}
vector<int> out[3];
for (auto& o : arr) {
int res = cb(o);
if (res == i) {
out[0].push_back(o);
} else if (res == j) {
out[1].push_back(o);
} else {
assert(res == k);
out[2].push_back(o);
}
}
if (max({sz(out[0]), sz(out[1]), sz(out[2])}) > p3 / 3) {
return;
}
assert(sz(out[0]) + sz(out[1]) + sz(out[2]) == sz(arr));
ans =
min(ans, 1 + max({dp(out[0]), dp(out[1]), dp(out[2])}));
};
go([&](int o) -> int { return q_lightest(o, i, j, k); });
go([&](int o) -> int { return q_heaviest(o, i, j, k); });
go([&](int o) -> int { return q_median(o, i, j, k); });
for (int d = 0; d < 6; d++) {
if (d == i || d == j || d == k) {
continue;
}
go([&](int o) -> int {
return q_next_lightest(o, i, j, k, d);
});
}
}
}
}
return ans;
}
void init(int) {
{
mt19937_64 cowng(1412);
for (auto& a : r_vals) {
a = cowng();
}
}
vector<int> perm(6);
iota(begin(perm), end(perm), 0);
do {
perms.push_back(perm);
} while (next_permutation(begin(perm), end(perm)));
for (int i = 0; i < 720; i++) {
for (int j = 0; j < 720; j++) {
auto tmp = perms[i];
for (auto& a : tmp) {
a = perms[j][a];
}
p_mul[i][j] =
int(lower_bound(begin(perms), end(perms), tmp) - perms.begin());
}
}
vector<int> arr(720);
iota(begin(arr), end(arr), 0);
arr.erase(remove_if(begin(arr), end(arr),
[&](int o) -> bool {
return q_next_lightest(o, 0, 1, 2, 3) != 0;
}),
arr.end());
dbg(dp({}));
dbg(sz(arr));
dbg(dp(arr));
dbg(sz(memo));
}
void print(vector<int> arr) {
if (sz(arr) <= 1) {
vector<int> ans(6);
auto c_arr = perms[arr[0]];
for (int i = 0; i < 6; i++) {
ans[c_arr[i]] = i + 1;
}
answer(ans.data());
return;
}
int p3 = 1;
while (p3 < sz(arr)) {
p3 *= 3;
}
int ans = dp(arr);
dbg(ans);
for (int i = 0; i < 6; i++) {
for (int j = i + 1; j < 6; j++) {
for (int k = j + 1; k < 6; k++) {
auto go = [&](auto cb) -> bool {
vector<int> out[3];
for (auto& o : arr) {
int res = cb(o);
if (res == i) {
out[0].push_back(o);
} else if (res == j) {
out[1].push_back(o);
} else {
assert(res == k);
out[2].push_back(o);
}
}
if (max({sz(out[0]), sz(out[1]), sz(out[2])}) > p3 / 3) {
return false;
}
assert(sz(out[0]) + sz(out[1]) + sz(out[2]) == sz(arr));
if (1 + max({dp(out[0]), dp(out[1]), dp(out[2])}) == ans) {
return true;
}
return false;
};
if (go([&](int o) -> int { return q_lightest(o, i, j, k); })) {
int res = G.q_lightest(i, j, k);
arr.erase(remove_if(begin(arr), end(arr),
[&](int o) -> bool {
return q_lightest(o, i, j, k) !=
res;
}),
arr.end());
print(arr);
return;
}
if (go([&](int o) -> int { return q_heaviest(o, i, j, k); })) {
int res = G.q_heaviest(i, j, k);
arr.erase(remove_if(begin(arr), end(arr),
[&](int o) -> bool {
return q_heaviest(o, i, j, k) !=
res;
}),
arr.end());
print(arr);
return;
}
if (go([&](int o) -> int { return q_median(o, i, j, k); })) {
int res = G.q_median(i, j, k);
arr.erase(remove_if(begin(arr), end(arr),
[&](int o) -> bool {
return q_median(o, i, j, k) != res;
}),
arr.end());
print(arr);
return;
}
for (int d = 0; d < 6; d++) {
if (d == i || d == j || d == k) {
continue;
}
if (go([&](int o) -> int {
return q_next_lightest(o, i, j, k, d);
})) {
int res = G.q_next_lightest(i, j, k, d);
arr.erase(remove_if(begin(arr), end(arr),
[&](int o) -> bool {
return q_next_lightest(o, i, j,
k, d) !=
res;
}),
arr.end());
print(arr);
return;
}
}
}
}
}
assert(false);
}
void orderCoins() {
vector<int> arr(720);
iota(begin(arr), end(arr), 0);
print(arr);
}
