#include <iostream>
#include <fstream>
#include <sstream>
#include <vector>
using namespace std;

#define dec(c) {x=(c)%p;y=(c)/p;}
#define enc(x,y) ((y)*p+(x))

int p;

int  id(int t){ return t; }
int idi(int t){ return t; }

int  rot(int t){ int x,y;dec(t); return enc(y,p-1-x); }
int roti(int t){ int x,y;dec(t); return enc(p-1-y,x); }

int  sym(int t){ int x,y;dec(t); return enc(p-1-x,y); }
int symi(int t){ int x,y;dec(t); return enc(p-1-x,y); }

int  bhsym(int t){ int x,y;dec(t); return (y<p/2)?enc(x,y):enc(p-1-x,y); }
int bhsymi(int t){ int x,y;dec(t); return (y<p/2)?enc(x,y):enc(p-1-x,y); }

int  bvsym(int t){ int x,y;dec(t); return (y<p/2)?enc(x,y):enc(x,3*p/2-1-y); }
int bvsymi(int t){ int x,y;dec(t); return (y<p/2)?enc(x,y):enc(x,3*p/2-1-y); }

int  div(int t){ int x,y;dec(t); return enc(x,(y/2)+p/2*(y%2)); }
int divi(int t){ int x,y;dec(t); return enc(x,((2*y)%p)+(2*y/p)); }

int mixi(int t){ int x,y;dec(t); return enc(x/2+(y%2)*p/2,y+x%2-y%2); }
int  mix(int t){ int x,y;dec(t); int a=x/(p/2),b=y%2; return enc(2*x-p*a+b,y+a-b); }

int gcd(int a,int b)
{
  return b==0?a:gcd(b,a%b);
}

int lcm(int a,int b)
{
  long long t=(long long)a*(long long)b;
  return t/(long long)gcd(a,b);
}

int main()
{
  ifstream cin("pixel.in");
  for (;cin>>p,p!=0;){
    cin.ignore(1024,'\n');
    string str;
    getline(cin,str);

    //cout<<"*** "<<str<<endl;

    vector<int> fs;
    istringstream iss(str);
    for (string key;iss>>key;){
      int inv=0;
      int tt=0;
      for(int i=key.length()-1;i>=0;i--){
        if (key[i]=='-'){
          inv^=1;
        }
        else{
          tt=i;
          break;
        }
      }
      key=key.substr(0,tt+1);
      int fc=0;
      if (key=="rot") fc=0;
      else if (key=="sym") fc=1;
      else if (key=="bhsym") fc=2;
      else if (key=="bvsym") fc=3;
      else if (key=="div") fc=4;
      else if (key=="mix") fc=5;
      else if (key=="id") fc=6;
      else abort();
      fc=fc*2+inv;
      fs.push_back(fc);
    }

    vector<int> _map(p*p);
    for (int i=0;i<p*p;i++){
      int t=i;
      for (int j=fs.size()-1;j>=0;j--){
        switch(fs[j]){
        case 0:  t=rot(t);break;
        case 1:  t=roti(t);break;
        case 2:  t=sym(t);break;
        case 3:  t=symi(t);break;
        case 4:  t=bhsym(t);break;
        case 5:  t=bhsymi(t);break;
        case 6:  t=bvsym(t);break;
        case 7:  t=bvsymi(t);break;
        case 8:  t=div(t);break;
        case 9:  t=divi(t);break;
        case 10: t=mix(t);break;
        case 11: t=mixi(t);break;
        case 12: t=id(t);break;
        case 13: t=idi(t);break;
        }
      }
      assert(t<p*p);
      _map[i]=t;
    }
/*
    for (int y=0;y<p;y++){
      for (int x=0;x<p;x++)
        cout<<(char)('A'+_map[enc(x,y)]);
      cout<<endl;
    }
*/
    int ans=1;
    vector<bool> pass(p*p,false);
    for (int i=0;i<p*p;i++){
      if (pass[i]) continue;
      int len=0;
      int t=i;
      while(!pass[t]){
        pass[t]=true;
        t=_map[t];
        len++;
      }
      //cout<<"*** "<<len<<endl;
      ans=lcm(ans,len);
    }
    cout<<ans<<endl;
  }
  return 0;
}