#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iterator>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#include <fstream>
#include <iomanip>
#include <cassert>
#include <utility>
#include <memory>
#include <functional>
#include <deque>
#include <cctype>
#include <ctime>
#include <numeric>
#include <list>
#include <iomanip>

#if __cplusplus >= 201103L
#include <array>
#include <tuple>
#include <initializer_list>
#include <forward_list>

#define cauto const auto&
#else

#endif

using namespace std;


typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef vector<int> vint;
typedef vector<vector<int> > vvint;
typedef vector<long long> vll, vLL;
typedef vector<vector<long long> > vvll, vvLL;

#define VV(T) vector<vector< T > >

template <class T>
void initvv(vector<vector<T> > &v, int a, int b, const T &t = T()){
    v.assign(a, vector<T>(b, t));
}

template <class F, class T>
void convert(const F &f, T &t){
    stringstream ss;
    ss << f;
    ss >> t;
}

#undef _P
#define _P(...) (void)printf(__VA_ARGS__)
#define reep(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) reep((i),0,(n))
#define ALL(v) (v).begin(),(v).end()
#define PB push_back
#define F first
#define S second
#define mkp make_pair
#define RALL(v) (v).rbegin(),(v).rend()
#define DEBUG
#ifdef DEBUG
#define dump(x)  cout << #x << " = " << (x) << endl;
#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#else
#define dump(x) 
#define debug(x) 
#endif

#define MOD 1000000007LL
#define EPS 1e-8
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
#define maxs(x,y) x=max(x,y)
#define mins(x,y) x=min(x,y)

map<string,int> dict;

//saikoro
 
typedef vector<int> Dice;
enum {TOP, FRONT, RIGHT, LEFT, BACK, BOTTOM};
#define rotate_swap(x, a, b, c, d) swap(x[a], x[b]); swap(x[b], x[c]); swap(x[c], x[d]);
 
void rotate_r(Dice& dice) {rotate_swap(dice, TOP, LEFT, BOTTOM, RIGHT);}
void rotate_l(Dice& dice) {rotate_swap(dice, TOP, RIGHT, BOTTOM, LEFT);}
void rotate_f(Dice& dice) {rotate_swap(dice, TOP, BACK, BOTTOM, FRONT);}
void rotate_b(Dice& dice) {rotate_swap(dice, TOP, FRONT, BOTTOM, BACK);}
void rotate_w(Dice& dice) {rotate_swap(dice, BACK, LEFT, FRONT, RIGHT);}
void rotate_c(Dice& dice) {rotate_swap(dice, BACK, RIGHT, FRONT, LEFT);}
 
vector<Dice> generate_all(Dice dice) {
 	vector<Dice> res;
  	for (int i = 0; i < 6; ++i) {
    	for (int j = 0; j < 4; ++j){
    		res.emplace_back(dice), rotate_w(dice);
    	}
	    if (i % 2) rotate_f(dice);
	    else rotate_r(dice);
	}
	return res;
}


void mainmain(){
	dict["Red"] = 0;
	dict["Yellow"] = 1;
	dict["Blue"] = 2;
	dict["Magenta"] = 3;
	dict["Green"] = 4;
	dict["Cyan"] = 5;
	int n;
	while(cin>>n,n){
		vector<Dice> v(n);
		rep(i,n){
			v[i] = Dice(6);
			rep(j,6){
				string s;
				cin>>s;
				v[i][j] = dict[s];
			}
		}
		int cnt = 0;
		rep(i,n){
			bool ok = true;
			rep(j,i){
				vector<Dice> tmp = generate_all(v[j]);
				rep(k, tmp.size()){
					if(tmp[k] == v[i]) ok = false;
				}
			}
			if(ok){
				cnt++;
			}
		}
		cout << n - cnt << endl;
	}
}


signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout<<fixed<<setprecision(20);
    mainmain();
}

Measured memory_bytes: 3144