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

//#define int long long

typedef pair<int,int>pint;
typedef vector<int>vint;
#define pb push_back
#define mp make_pair
#define rep(i,n) for(int i=0;i<(n);i++)
template<class T,class U>void chmin(T &t,U f){if(t>f)t=f;}
template<class T,class U>void chmax(T &t,U f){if(t<f)t=f;}

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;
  }
  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) {
    int tmp = id[a];
    id[a] = id[b]; id[b] = id[c];
    id[c] = id[d]; id[d] = tmp;
  }
  T var[6];
  int id[6];
};


int main(){
    int N;
    while(scanf("%d",&N),N){
        vector<dice<string> >vec;
        int cnt=0;
        while(N--){
            dice<string> b;
            cin>>b[TOP];
            cin>>b[FRONT];
            cin>>b[RIGHT];
            cin>>b[LEFT];
            cin>>b[BACK];
            cin>>b[BOTTOM];
            bool ok=true;
            rep(i,vec.size())if(vec[i].equivalent_to(b))ok=false;
            if(ok)vec.pb(b);
            else cnt++;
        }
        cout<<cnt<<endl;
    }
    return 0;
}