#include <iostream>
#include <algorithm>
#include <vector>
#include <map>

using namespace std;

enum FACE { TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT };
template <class T>
class dice {
public:
  dice() {
    id[TOP] = 0; id[FRONT] = 1; id[LEFT] = 2;
    id[RIGHT] = 3; id[BACK] = 4; id[BOTTOM] = 5;
  }
  dice(int t, int f, int l, int r, int b, int m) {
    id[TOP] = t; id[FRONT] = f; id[LEFT] = l;
    id[RIGHT] = r; id[BACK] = b; id[BOTTOM] = m;
  }
  T& operator[] (FACE f) { return var[id[f]]; }
  const T& operator[] (FACE f) const { return var[id[f]]; }
  bool operator==(const dice<T>& b) const {
    const dice<T> &a = *this;
    return a[TOP] == b[TOP] && a[BOTTOM] == b[BOTTOM] &&
           a[FRONT] == b[FRONT] && a[BACK] == b[BACK] &&
           a[LEFT] == b[LEFT] && a[RIGHT] == b[RIGHT];
  }
  void roll_x() { roll(TOP, BACK, BOTTOM, FRONT); }
  void roll_y() { roll(TOP, LEFT, BOTTOM, RIGHT); }
  void roll_z() { roll(FRONT, RIGHT, BACK, LEFT); }
  vector<dice> all_rolls() {
    vector<dice> ret;
    for (int k = 0; k < 6; (k&1?roll_y():roll_x()),++k)
      for (int i = 0; i < 4; roll_z(), ++i)
        ret.push_back(*this);
    return ret;
  }
  bool equivalent_to(const dice& di) {
    for (int k = 0; k < 6; (k&1?roll_y():roll_x()),++k)
      for (int i = 0; i < 4; roll_z(), ++i)
        if (*this == di) return true;
    return false;
  }
private:
  void roll(FACE a, FACE b, FACE c, FACE d) {
    T tmp = id[a];
    id[a] = id[b]; id[b] = id[c];
    id[c] = id[d]; id[d] = tmp;
  }
  T var[6];
  int id[6];
};

string cols[]={"Red", "Yellow", "Blue", "Magenta", "Green", "Cyan"};
map<string, int> mp;

int main() {
  
  for(int i=0; i<6; i++) mp[cols[i]] = i;
  int N;
  while(cin >> N && N) {
    vector<dice<int> > d;
    for(int i=0; i<N; i++) {
      vector<int> v(6);
      for(int j=0; j<6; j++) {
        string s; cin >> s; v[j] = mp[s];
      }
      d.push_back(dice<int>(v[0],v[1],v[2],v[3],v[4],v[5]));
    }
    
    int cnt = 0;
    bool update = true;
    while(update) {
      update = false;
      for(int i=0; i<d.size(); i++) {
        for(int j=i+1; j<d.size(); j++) {
          if(d[i].equivalent_to(d[j])) {
            cnt ++;
            d.erase(d.begin()+i); update = true; goto NEXT;
          }
        }
      }
    NEXT:;
    }
    cout << N-cnt << endl;
  }
  
  return 0;
}