#include<bits/stdc++.h>
#include "scales.h"
using namespace std;
using ll = long long;
#define sz(x) int((x).size())
ll pw3[30];
const int n = 6;
const int inf = 1e9;
using st = array<int, 6>;
using op = tuple<int,int,int,int,int>;
map<vector<st>, op> usedop;
array<vector<st>, 3> getNext(vector<st> cur, op op) {
auto [t, a, b, c, d] = op;
array<vector<st>, 3> next{{}};
if (t == 0) {
for (auto& i : cur) {
int mn = min({i[a], i[b], i[c]});
if (i[a] == mn)
next[0].push_back(i);
else if (i[b] == mn)
next[1].push_back(i);
else
next[2].push_back(i);
}
} else if (t == 1) {
for (auto& i : cur) {
int mx = max({i[a], i[b], i[c]});
if (i[a] == mx)
next[0].push_back(i);
else if (i[b] == mx)
next[1].push_back(i);
else
next[2].push_back(i);
}
} else {
for (auto& i : cur) {
array cur{i[a], i[b], i[c]};
sort(cur.begin(), cur.end());
if (i[a] == cur[1])
next[0].push_back(i);
else if (i[b] == cur[1])
next[1].push_back(i);
else
next[2].push_back(i);
}
}
return next;
}
int cost(array<vector<st>, 3> pos) {
return max({pos[0].size(), pos[1].size(), pos[2].size()});
}
int rec(vector<st> pos, int qleft) {
if (pw3[qleft] < sz(pos)) return false;
if (pos.size() <= 1) return true;
array<vector<st>, 3> best;
int bestx = inf;
op bestq;
auto tryAccept =[&](op op) {
auto next = getNext(pos, op);
int mx = max({next[0].size(), next[1].size(), next[2].size()});
if (mx < bestx) {
bestx = mx;
best = next;
bestq = op;
}
};
for (int a = 0; a < n; a++) {
for (int b = a+1; b < n; b++) {
for (int c = b+1; c < n; c++) {
tryAccept({0, a, b, c, -1});
tryAccept({1, a, b, c, -1});
tryAccept({2, a, b, c, -1});
}
}
}
if (!rec(best[0], qleft-1)) return false;
if (!rec(best[1], qleft-1)) return false;
if (!rec(best[2], qleft-1)) return false;
usedop[pos] = bestq;
return true;
}
void init(int T) {
pw3[0] = 1;
for (int i = 1; i < 30; i++)
pw3[i] = pw3[i-1] * 3;
vector<st> pos;
st cur;
iota(cur.begin(), cur.end(), 0);
do {
pos.push_back(cur);
} while (next_permutation(cur.begin(), cur.end()));
cout << rec(pos, 8) << endl;
}
void orderCoins() {
vector<st> pos;{
st cur;
iota(cur.begin(), cur.end(), 0);
do {
pos.push_back(cur);
} while (next_permutation(cur.begin(), cur.end()));}
while (pos.size() > 1) {
cout << "pos.size()=" << pos.size() << endl;
assert(usedop.count(pos));
auto op = usedop[pos];
auto[t, a, b, c, d] = op;
auto next = getNext(pos, op);
a++;b++;c++;
if (t == 0) {
int ans = getLightest(a, b, c);
if (ans == a) pos = next[0];
if (ans == b) pos = next[1];
if (ans == c) pos = next[2];
} else if (t == 1) {
int ans = getHeaviest(a, b, c);
if (ans == a) pos = next[0];
if (ans == b) pos = next[1];
if (ans == c) pos = next[2];
} else {
int ans = getMedian(a, b, c);
if (ans == a) pos = next[0];
if (ans == b) pos = next[1];
if (ans == c) pos = next[2];
}
}
int w[6];
for (int i = 0; i < 6; i++) {
w[pos[0][i]] = i+1;
}
answer(w);
}
