#include "scales.h"
#include <bits/stdc++.h>

using namespace std;
const int inf = (int)1e9;
vector<array<int, 4>> tr, rt;

map<vector<vector<int>>, pair<int, array<int, 5>>> dp;
int it = 0;
int go(vector<vector<int>> v, bool ok = 0, int pot = 729, int lev = 0) {
    it++;
    assert((int)v.size() <= pot);
    if(dp.count(v)) return dp[v].first;
    if(v.empty()) return 0;
    if(v.size() == 1) {
        if(ok) {
            int w[6];
            for(int i = 0; i < 6; i++) {
                w[i] = v[0][i];
            }
            answer(w);
        }
        return 0;
    }
    array<int, 5> ans = {inf, inf,  inf, inf, inf};
    array<int, 5> ans1 = {inf, inf,  inf, inf, inf};
    for(auto [x, y, z, tp] : tr) {
        vector<vector<int>> a, b, c;
        for(auto f : v) {
            vector<int> pos(7);
            for(int i = 0; i < 6; i++) {
                pos[f[i]] = i;
            }
            vector<int> tr;
            tr = {x, y, z};
            sort(tr.begin(), tr.end(), [&](int i, int j){return pos[i] < pos[j];});
            if(tr[tp] == x) a.push_back(f);
            else if(tr[tp] == y) b.push_back(f);
            else c.push_back(f);
        }
        if(max({(int)a.size(), (int)b.size(), (int)c.size()}) > pot / 3 || max({(int)a.size(), (int)b.size(), (int)c.size()}) == (int)v.size()) continue;
        vector<int> gg;
        int val = max({go(a, 0, pot / 3, lev + 1), go(b, 0, pot / 3, lev + 1), go(c, 0, pot / 3, lev + 1)})  + 1;
        if(val + lev == 6) {
            ans = {val, x, y, z, tp};
            break;
        }
    }
    for(auto [a, b, c, d] : rt) {
        vector<vector<int>> _a, _b, _c;
        for(auto f : v) {
            vector<int> pos(7);
            for(int i = 0; i < 6; i++) {
                pos[f[i]] = i;
            }
            vector<int> tr;
            tr = {a, b, c, d};
            sort(tr.begin(), tr.end(), [&](int i, int j){return pos[i] < pos[j];});
            if(tr[3] == d) {
                if(tr[0] == a) _a.push_back(f);
                else if(tr[0] == b) _b.push_back(f);
                else _c.push_back(f); 
            } else {
                int nx = -1;
                for(int i = 0; i < 4; i++) {
                    if(tr[i] == d) {
                        nx = tr[i + 1];
                        break;
                    }
                }
                if(nx == a) _a.push_back(f);
                else if(nx == b) _b.push_back(f);
                else _c.push_back(f); 
            }
        }
        int mx = max({(int)_a.size(), (int)_b.size(), (int)_c.size()});
        if(mx > pot / 3 || mx == (int)v.size()) continue;
        int val = max({go(_a, 0, pot / 3, lev + 1), go(_b, 0, pot / 3, lev + 1), go(_c, 0, pot / 3, lev + 1)}) + 1;
        if(val + lev == 6) {
            ans1 = {val, a, b, c, d};
            break;
        }
    }
    ans = min(ans, ans1);
    if(ans[0] < ans1[0]) {
        dp[v].first = ans[0];
        dp[v].second = {0, ans[1], ans[2], ans[3], ans[4]};
    } else {
        ans = ans1;
        dp[v].first = ans[0];
        dp[v].second = {1, ans[1], ans[2], ans[3], ans[4]};
    }
    return ans[0];
}
void init(int T) {
    for(int i = 1; i <= 6; i++) {
        for(int j = i + 1; j <= 6; j++) {
            for(int k = j + 1; k <= 6; k++) {
                for(int tp = 0; tp < 3; tp++) {
                    tr.push_back({i, j, k, tp});
                }
            }
        }
    }
    for(int i = 1; i <= 6; i++) {
        for(int j = i + 1; j <= 6; j++) {
            for(int k = j + 1; k <= 6; k++) {
                for(int e = 1; e <= 6; e++) if(e != i && e != j && e != k) {
                    rt.push_back({i, j, k, e});
                }
            }
        }
    }
    vector<int> f(6);
    iota(f.begin(), f.end(), 1);
    vector<vector<int>> a;
    do
    {
        a.push_back(f);
    } while (next_permutation(f.begin(), f.end()));
    go(a, 0);
}
void orderCoins() {
    vector<int> f(6);
    iota(f.begin(), f.end(), 1);
    vector<vector<int>> v;
    do
    {
        v.push_back(f);
    } while (next_permutation(f.begin(), f.end()));
    while(v.size() > 1) {
        vector<vector<int>> nx;
        if(dp[v].second[0] == 0) {
            auto [res, x, y, z, tp] = dp[v].second;
            int val;
            if(!tp) val = getLightest(x, y, z);
            else if(tp == 1) val = getMedian(x, y, z);
            else val = getHeaviest(x, y, z);
            for(auto f : v) {
                vector<int> pos(7);
                for(int i = 0; i < 6; i++) {
                    pos[f[i]] = i;
                }
                vector<int> tr;
                tr = {x, y, z};
                sort(tr.begin(), tr.end(), [&](int i, int j){return pos[i] < pos[j];});
                if(val == tr[tp]) nx.push_back(f);
            }
        } else {
            auto [res, a, b, c, d] = dp[v].second;
            // cerr << a << ' ' << b << ' ' << c << ' ' << d << '\n';
            int val = getNextLightest(a, b, c, d);
            for(auto f : v) {
                vector<int> pos(7);
                for(int i = 0; i < 6; i++) {
                    pos[f[i]] = i;
                }
                vector<int> tr;
                tr = {a, b, c, d};
                sort(tr.begin(), tr.end(), [&](int i, int j){return pos[i] < pos[j];});
                if(tr[3] == d) {
                    if(val == tr[0]) {
                        nx.push_back(f);
                    }
                } else {
                    int nt = -1;
                    for(int i = 0; i < 4; i++) {
                        if(tr[i] == d) {
                            nt = tr[i + 1];
                            break;
                        }
                    }
                    if(nt == val) {
                        nx.push_back(f);
                    } 
                }
            }
        }
        v = nx;
    }
    int w[6];
    for(int i = 0; i < 6; i++) {
        w[i] = v[0][i];
    }
    answer(w);
}