F

#include <iostream>
#include <set>
#include <map>
#include <vector>
#include <algorithm>

using namespace std;


int main() {
	int m;
	cin >> m;
	vector<vector<int> > a(m, vector<int>(m));
	for (int i = 0; i < m; i++) {
		for (int j = 0; j < m; j++) {
			cin >> a[i][j];
		}
	}
	bool ass = 1;
	for (int i = 0; i < m && ass; i++) {
		for (int j = i + 1; j < m && ass; j++) {
			for (int q = j + 1; q < m && ass; q++) {
				if (a[i][a[j][q]] != a[a[i][j]][q]) {
					ass = 0;
				}
				if (a[j][a[q][i]] != a[a[j][q]][i]) {
					ass = 0;
				}
				if (a[q][a[i][j]] != a[a[q][i]][j]) {
					ass = 0;
				}

				if (a[i][a[q][j]] != a[a[i][q]][j]) {
					ass = 0;
				}
				if (a[j][a[i][q]] != a[a[j][i]][q]) {
					ass = 0;
				}
				if (a[q][a[j][i]] != a[a[q][j]][i]) {
					ass = 0;
				}
			}
		}
	}

	bool ed = 0;
	bool ned = -1;
	for (int i = 0; i < m; i++) {
		bool e = 1;
		for (int j = 0; j < m; j++) {
			if (a[i][j] != a[j][i] || a[j][i] != j + 1) {
				e = 0;
				break;
			}
		}
		if (e) {
			ed = 1;
			ned = i + 1;
			break;
		}
	}

	bool komp = 1;
	for (int i  =0; i < m && komp; i++){
		for (int j = 0; j < m && komp; j++) {
			if (a[i][j] != a[j][i]) {
				komp = 0;
			}
		}
	}

	bool obr = 0;
	if (ed) {
		int k = 0;
		for (int i = 0; i < m; i++) {
			bool e = 0;
			for (int j = 0; j < m; j++) {
				if (a[i][j] == a[j][i] && a[i][j] == ned) {
					e = 1;
				}
			}
			if (e) {
				k++;
			}
		}
		if (k == m) {
			obr = 1;
		}
	}

	if (ass) {
		if (komp) {
			if (ed) {
				if (obr) {
					cout << "abelian group";
				}
				else {
					cout << "commutative monoid";
				}
			}
			else {
				cout << "commutative semigroup";
			}
		}
		else {
			if (ed) {
				if (obr) {
					cout << "group";
				}
				else {
					cout << "monoid";
				}
			}
			else {
				cout << "semigroup";
			}
		}
	}
	else {
		if (komp) {
			cout << "commutative groupoid";
		}
		else {
			cout << "groupoid";
		}
	}

	return 0;
}