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

#define pb(n) push_back(n)
#define fi first
#define se second
#define all(r) (r).begin(),(r).end()
#define vmax(ary) *max_element(all(ary))
#define vmin(ary) *min_element(all(ary))
#define debug(x) cout<<#x<<": "<<x<<endl
#define fcout(n) cout<<fixed<<setprecision((n))
#define scout(n) cout<<setw(n)
#define vary(type,name,size,init) vector< type> name(size,init)
#define vvl(v,w,h,init) vector<vector<ll>> v(w,vector<ll>(h,init))
#define mp(a,b) make_pair(a,b)

#define rep(i,n) for(int i = 0; i < (int)(n);++i)
#define REP(i,a,b) for(int i = (a);i < (int)(b);++i)
#define repi(it,array) for(auto it = array.begin(),end = array.end(); it != end;++it)
#define repa(n,array) for(auto &n :(array))

using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using dict = map<string,int>;
using pii = pair<int,int> ;
using pll = pair<ll,ll> ;

const int mod = 1000000007;
constexpr int inf = ((1<<30)-1)*2+1 ;
constexpr double PI = acos(-1.0) ;
double eps = 1e-10 ;
const int dy[] = {-1,0,1,0,1,-1,1,-1};
const int dx[] = {0,-1,0,1,1,-1,-1,1};

inline bool value(int x,int y,int w,int h){
  return (x >= 0 && x < w && y >= 0 && y < h);
}

template<typename T>
void Unique(vector<T> &v){
  sort(all(v));
  v.erase(unique(all(v)),v.end());
}
template<typename T,typename U>
ll FindErase(T &v,U tar){
  ll cnt = 0;
  for(auto it = v.begin(); it != v.end();){
    if(*it == tar){
      it = v.erase(it);
      ++cnt;
    }
    else{
      ++it;
    }
  }
  return cnt;
}

enum{
  t = 0,f ,r ,b ,l ,d ,
};
template<typename S>
class Dice{
  public:
    array<S,6> D;
    Dice(){
    }
    Dice(array<S,6> d){
      copy(all(D),d.begin());
    }
    void Spin(int dir){
      if(dir == l){//
        swap(D[t],D[r]);
        swap(D[r],D[d]);
        swap(D[d],D[l]);
      }
      else if(dir == r){
        swap(D[t],D[l]);
        swap(D[l],D[d]);
        swap(D[d],D[r]);
      }
      else if(dir == f){
        swap(D[t],D[b]);
        swap(D[b],D[d]);
        swap(D[d],D[f]);
      }
      else if(dir == b){
        swap(D[t],D[f]);
        swap(D[f],D[d]);
        swap(D[d],D[b]);
      }
      else if(dir == d){//leftspin
        swap(D[f],D[r]);
        swap(D[r],D[b]);
        swap(D[b],D[l]);
      }
      else if(dir == t){
        swap(D[f],D[l]);
        swap(D[l],D[b]);
        swap(D[b],D[r]);
      }
    }
    void MatchDice(int T,int F){
      rep(i,4){
        Spin(r);
        if(D[t] == T)break;
      }
      if(D[t] != T){
        rep(i,4){
          Spin(f);
          if(D[t] == T)break;
        }
      }
      rep(i,4){
        Spin(t);
        if(D[f] == F) break;
      }
    }
    S& operator[](const int i){
      return D[i];
    }
    bool operator==(Dice& di2){
      rep(i,4){
        di2.Spin(r);
        rep(j,4){
          di2.Spin(t);
          rep(k,4){
            di2.Spin(r);
            if(D == di2.D){
              return true;
            }
          }
        }
      }
      return false;
    }
    friend ostream& operator<<(ostream& os,const Dice& di){
      os << "t f r l b d\n" ;
      rep(i,6){
        if(i) os << ' ';
        os << di.D[i] ;
      }
      return os;
    }
};

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll n;
  while(cin >> n && n){
    vector<Dice<string>> di(n);
    vector<Dice<string>> st;
    rep(i,n){
      cin >> di[i][t] >> di[i][f] >> di[i][r] >> di[i][l] >> di[i][b] >> di[i][d] ;
      if(st.size() == 0){
        st.push_back(di[i]);
      }
      else{
        rep(j,st.size()){
          if(st[j] == di[i]){
            break;
          }
          if(j == st.size()-1){
            st.push_back(di[i]);
          }
        }
      }
    }
    cout << n - st.size()<<endl;
  }
  return 0;
}

Measured memory_bytes: 3124