#include <iostream>
#include <string>
#include <vector>
#include <map>
#include <set>
using namespace std;

// http://www.prefield.com/algorithm/misc/dice.html
enum FACE { TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT };
class dice {
public:
	dice(int top,int front,int right,int left,int back,int bottom) {
		id[TOP] = top; id[FRONT] = front; id[RIGHT] = right;
		id[LEFT] = left; id[BACK] = back; id[BOTTOM] = bottom;
	}
	void roll_north() { roll(TOP, FRONT, BOTTOM, BACK); }
	void roll_south() { roll(TOP, BACK, BOTTOM, FRONT); }
	void roll_east() { roll(TOP, LEFT, BOTTOM, RIGHT); }
	void roll_west() { roll(TOP, RIGHT, BOTTOM, LEFT); }
	void roll_right() { roll(FRONT, LEFT, BACK, RIGHT); }
	void roll_left() { roll(FRONT, RIGHT, BACK, LEFT); }
	void all_rolls(set<long long> &s){
		for (int k = 0; k < 6; (k&1?roll_east():roll_north()),++k)
			for (int i = 0; i < 4; roll_right(), ++i)
				s.insert(((long long)id[TOP]<<40) | ((long long)id[FRONT]<<32) | (id[RIGHT]<<24) | (id[LEFT]<<16) | (id[BACK]<<8) | (id[BOTTOM]<<0));
	}
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;
	}
	int id[6];
};

int main(){
	string str;
	int d[6];
	int n,i,j,r;
	for(;cin>>n,n;){
		set<long long>s;
		for(r=i=0;i<n;i++){
			for(j=0;j<6;j++)cin>>str,d[j]=str[0];
			long long x=((long long)d[0]<<40) | ((long long)d[1]<<32) | (d[2]<<24) | (d[3]<<16) | (d[4]<<8) | (d[5]<<0);
			if(s.find(x)!=s.end())r++;
			else{
				dice di(d[0],d[1],d[2],d[3],d[4],d[5]);
				di.all_rolls(s);
			}
		}
		cout<<r<<endl;
	}
}