#include "scales.h"
#include <bits/stdc++.h>
#define ll long long
using namespace std;
int p[7];
void getInit(vector<int> &v)
{
for (int i = 0; i < 6; i++)
p[v[i]] = i;
}
int getM(int A, int B, int C, vector<int> &v)
{
getInit(v);
int mx = max({p[A], p[B], p[C]}), mi = min({p[A], p[B], p[C]});
if (mi < p[A] && p[A] < mx)
return A;
if (mi < p[B] && p[B] < mx)
return B;
return C;
}
int getH(int A, int B, int C, vector<int> &v)
{
getInit(v);
int mx = max({p[A], p[B], p[C]});
if (p[A] == mx)
return A;
if (p[B] == mx)
return B;
return C;
}
int getL(int A, int B, int C, vector<int> &v)
{
getInit(v);
int mi = min({p[A], p[B], p[C]});
if (p[A] == mi)
return A;
if (p[B] == mi)
return B;
return C;
}
int getNL(int A, int B, int C, int D, vector<int> &v)
{
int mi = getL(A, B, C, v),
me = getM(A, B, C, v),
mx = getH(A, B, C, v);
if (p[D] < p[mi])
return mi;
if (p[D] < p[me])
return me;
if (p[D] < p[mx])
return mx;
return mi;
}
/*
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);
*/
struct op
{
int type, a, b, c, d, out;
} tree[800][6];
bool brute(vector<pair<vector<int>, int>> &state, int dep)
{
// cout << "brute " << sz << '\n';
int sz = state.size();
if (sz <= 1)
return 1;
for (int D = 1; D <= 6; D++)
for (int A = 1; A <= 6; A++)
for (int B = A + 1; B <= 6; B++)
for (int C = B + 1; C <= 6; C++)
if (A != D && B != D && C != D)
{
vector<pair<vector<int>, int>> space[7];
for (auto [v, i] : state)
space[getNL(A, B, C, D, v)].emplace_back(make_pair(v, i));
bool good = 1;
for (int k = 1; k <= 6; k++)
if (space[k].size() > (sz + 2) / 3)
good = 0;
if (good)
{
bool solve = 1;
for (int k = 1; k <= 6; k++)
if (!space[k].empty())
solve &= brute(space[k], dep + 1);
if (solve)
{
for (int k = 1; k <= 6; k++)
for (auto [v, i] : space[k])
tree[i][dep] = {2, A, B, C, D, k};
return 1;
}
}
}
for (int A = 1; A <= 6; A++)
for (int B = A + 1; B <= 6; B++)
for (int C = B + 1; C <= 6; C++)
{
vector<pair<vector<int>, int>> space[7];
for (auto [v, i] : state)
{
for (int i = 0; i < 6; i++)
p[i + 1] = v[i];
space[getM(A, B, C, v)].emplace_back(make_pair(v, i));
}
bool good = 1;
for (int k = 1; k <= 6; k++)
if (space[k].size() > (sz + 2) / 3)
good = 0;
if (good)
{
bool solve = 1;
for (int k = 1; k <= 6; k++)
if (!space[k].empty())
solve &= brute(space[k], dep + 1);
if (solve)
{
for (int k = 1; k <= 6; k++)
for (auto [v, i] : space[k])
tree[i][dep] = {1, A, B, C, 0, k};
return 1;
}
}
}
return 0;
}
vector<pair<vector<int>, int>> allp;
void init(int T)
{
vector<int> v = {1, 2, 3, 4, 5, 6};
for (int i = 0; i < 720; i++)
{
allp.emplace_back(make_pair(v, i));
next_permutation(v.begin(), v.end());
}
brute(allp, 0);
}
void orderCoins()
{
vector<int> remain, tmp;
for (int i = 0; i < 720; i++)
remain.emplace_back(i);
for (int i = 0; i < 6; i++)
{
int j = remain.back(), res;
auto [t, a, b, c, d, o] = tree[j][i];
if (t == 1)
res = getMedian(a, b, c);
else
res = getNextLightest(a, b, c, d);
tmp.clear();
for (auto k : remain)
if (tree[k][i].out == res)
tmp.emplace_back(k);
swap(tmp, remain);
}
int ans[6];
for (int i = 0; i < 6; i++)
ans[i] = allp[remain[0]].first[i];
answer(ans);
}
