Cubos Coloridos

#include <bits/stdc++.h>
using namespace std;

struct Cube {
    int upper_face, lower_face;
    vector<int> middle_faces;
    Cube() { middle_faces = vector<int>(4); }

    vector<int> get_cube() {
        vector<int> c = middle_faces;
        c.push_back(upper_face);
        c.push_back(lower_face);
        return c;
    }

    void rotate_vert() {
        int temp_upper = upper_face;
        int temp_lower = lower_face;

        upper_face = middle_faces[0];
        lower_face = middle_faces[2];

        middle_faces[0] = temp_lower;
        middle_faces[2] = temp_upper;
    }

    void rotate_horiz() {
        middle_faces = vector<int> { middle_faces[1], middle_faces[2], middle_faces[3], middle_faces[0] };
    }
};


vector<Cube> cubes;
vector<int> father, sz;
int ans;

void gen(Cube a, int k, set<vector<int>> &possibilities) {
    if(k == 8) return;

    possibilities.insert(a.get_cube());

    Cube c = a, d = a;

    c.rotate_horiz();
    d.rotate_vert();

    gen(c, k + 1, possibilities);
    gen(d, k + 1, possibilities);
}

int find(int x) {
    if(x == father[x]) return x;
    return father[x] = find(father[x]);
}

void join(int x, int y) {
    x = find(x);  y = find(y);
    if(x == y) return;
    if(sz[x] > sz[y]) swap(x, y);
    father[x] = y;
    sz[y] += sz[x];
    ans--;
}

int32_t main() {

    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int n;
    while(cin >> n and n) {
        cubes = vector<Cube>(n);
        father = vector<int>(n);
        sz = vector<int>(n);
        ans = n;

        for(int i= 0; i < n; i++)
            father[i] = i, sz[i] = 1;

        map<vector<int>, int> existing_cube;

        for(int i = 0; i < n; i++) {
            cin >> cubes[i].upper_face;
            for(int j = 0; j < 4; j++)
                cin >> cubes[i].middle_faces[j];
            cin >> cubes[i].lower_face;

            set<vector<int>> possibilities;

            gen(cubes[i], 0, possibilities);

            for(auto c : possibilities) {
                if(existing_cube.count(c)) {
                    int j = existing_cube[c];
                    join(i, j);
                }
            }

            existing_cube[ cubes[i].get_cube() ] = i;
        }
        cout << ans << '\n';
    }

    return 0;
}