#include <iostream>
#include <fstream>
#include <sstream>
#include <vector>

#define N (1024)
#define Z(x,y) ((x) + (y) * n)
#define X(z) ((z) % n)
#define Y(z) ((z) / n)

using namespace std;

static int ff[N*N], *f = ff;
static int gg[N*N], *g = gg;
static int hh[N*N], *h = hh;
static int n;

int _rot(int x, int y)
{
	return Z(y, n - 1 - x);
}

int _sym(int x, int y)
{
	return Z(n - 1 - x, y);
}

int _bhsym(int x, int y)
{
	if(y < n / 2) x = n - 1 - x;
	return Z(x, y);
}

int _bvsym(int x, int y)
{
	if(y < n / 2) y = n / 2 - 1 - y;
	return Z(x, y);
}

int _div(int x, int y)
{
	return Z(x, (y / 2) + (y % 2) * (n / 2));
}

int _mix(int x, int y)
{
	int n2 = n / 2;
	int x0 = (x % n2) * 2 + (y % 2);
	int y0 = (x / n2) + (y - y % 2);
	return Z(x0, y0);
}

void apply(string name)
{
	int (*func)(int, int) = NULL;

	bool inv = false;

	if(name[name.length() - 1] == '-') {
		name = name.substr(0, name.length() - 1);
		inv = true;
	}

	if(name == "rot"  ) func = _rot  ;
	if(name == "sym"  ) func = _sym  ;
	if(name == "bhsym") func = _bhsym;
	if(name == "bvsym") func = _bvsym;
	if(name == "div"  ) func = _div  ;
	if(name == "mix"  ) func = _mix  ;

	if(func == NULL) return;

	for(int y = 0; y < n; y++) {
		for(int x = 0; x < n; x++) {
			int z0 = Z(x, y);
			int z1 = func(x, y);
			if(inv) g[z0] = f[z1]; else g[z1] = f[z0];
		}
	}

	swap(f, g);
}

int cycle(int z0)
{
	int z = z0;

	for(int k = 1; /* infinite */; k++) {
		z = f[z];
		if(z == z0) return k;
	}
}

int power(int k)
{
	swap(f, g);

	for(int i = 0; i < n * n; i++)
		f[i] = i;

	while(k > 1) {
		if((k & 1) == 1) {
			for(int i = 0; i < n * n; i++)
				f[i] = g[f[i]];
		}

		for(int i = 0; i < n * n; i++)
			h[i] = g[g[i]];

		swap(g, h);
		k >>= 1;
	}

	for(int i = 0; i < n * n; i++)
		f[i] = g[f[i]];

	/*
	for(int y = 0; y < n; y++) {
		for(int x = 0; x < n; x++) {
			cout << "(" << X(f[Z(x,y)]) << "," << Y(f[Z(x,y)]) << ")";
		}
		cout << endl;
	}
	*/
}

int main(void)
{
	ifstream fin("pixel.in");

	while(fin >> n, n) {
		for(int i = 0; i < n * n; i++)
			f[i] = i;

		string line;
		getline(fin, line);
		getline(fin, line);
		istringstream iss(line);

		vector<string> verbs;
		string verb;
		while(iss >> verb) verbs.push_back(verb);

		for(int i = verbs.size() - 1; i >= 0; i--)
			apply(verbs[i]);

		int m = 1;

		for(int i = 0; i < n * n; i++) {
			int k = cycle(i);
			if(k > 1) { power(k); m *= k; }
		}

		cout << m << endl;
	}

	return 0;
}