AOJITP1_11_D.cpp

#include <bits/stdc++.h>
using namespace std;

using VS = vector<string>;    using LL = long long;
using VI = vector<int>;       using VVI = vector<VI>;
using PII = pair<int, int>;   using PLL = pair<LL, LL>;
using VL = vector<LL>;        using VVL = vector<VL>;

#define ALL(a)  begin((a)),end((a))
#define RALL(a) (a).rbegin(), (a).rend()
#define SZ(a) int((a).size())
#define SORT(c) sort(ALL((c)))
#define RSORT(c) sort(RALL((c)))
#define UNIQ(c) (c).erase(unique(ALL((c))), end((c)))
#define FOR(i, s, e) for (int(i) = (s); (i) < (e); (i)++)
#define FORR(i, s, e) for (int(i) = (s); (i) > (e); (i)--)
#define debug(x) cerr << #x << ": " << x << endl
const int INF = 1e9;                          const LL LINF = 1e16;
int DX[8] = { 0, 0, 1, -1, 1, 1, -1, -1 };    int DY[8] = { 1, -1, 0, 0, 1, -1, 1, -1 };

/* -----  2018/06/24  Problem: AOJ ITP1_11_D / Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_11_D  ----- */
/* ------問題------

Dice I と同様の方法で、入力された整数から n 個のサイコロをつくります。これらのサイコロが、全て異なるものかどうかを判定するプログラムを作成してください。同一かどうかの判定は Dice III の方法を用います。

-----問題ここまで----- */
/* -----解説等-----

3と一緒で判定をすれば良い。

----解説ここまで---- */


using uLL = unsigned long long;

const uLL MOD = 1e9;
//BEGIN CUT HERE
struct Dice {
	int s[6];
	void roll(char c) {
		//the view from above
		// N
		//W E
		// S
		//va[0]:top
		//va[1]:south
		//va[2]:east
		//va[3]:west
		//va[4]:north
		//va[5]:bottom
		int b;
		if (c == 'E') {
			b = s[0];
			s[0] = s[3];
			s[3] = s[5];
			s[5] = s[2];
			s[2] = b;
		}
		if (c == 'W') {
			b = s[0];
			s[0] = s[2];
			s[2] = s[5];
			s[5] = s[3];
			s[3] = b;
		}
		if (c == 'N') {
			b = s[0];
			s[0] = s[1];
			s[1] = s[5];
			s[5] = s[4];
			s[4] = b;
		}
		if (c == 'S') {
			b = s[0];
			s[0] = s[4];
			s[4] = s[5];
			s[5] = s[1];
			s[1] = b;
		}

		// migi neji 
		if (c == 'R') {
			b = s[1];
			s[1] = s[2];
			s[2] = s[4];
			s[4] = s[3];
			s[3] = b;
		}

		if (c == 'L') {
			b = s[1];
			s[1] = s[3];
			s[3] = s[4];
			s[4] = s[2];
			s[2] = b;
		}

	}
	int top() {
		return s[0];
	}
	int bottom() {
		return s[5];
	}
	uLL hash() {
		uLL res = 1;
		for (int i = 0; i < 6; i++) res = res * (MOD)+s[i];
		return res;
	}
	void print() {
		cout << "Dice num: ";
		FOR(i, 0, 6) {
			cout << s[i] << " ";
		}
		cout << "Hash: " << this->hash() << endl;
		cout << endl;
	}
	bool operator < (const Dice &x)const {
		FOR(i, 0, 6)if (x.s[i] < s[i])return true;
		return false;
	}

};
vector<Dice> makeDices(Dice d) {
	vector<Dice> res;
	for (int i = 0; i < 6; i++) {
		Dice t(d);
		if (i == 1) t.roll('N');
		if (i == 2) t.roll('S');
		if (i == 3) t.roll('S'), t.roll('S');
		if (i == 4) t.roll('L');
		if (i == 5) t.roll('R');
		for (int k = 0; k < 4; k++) {
			res.push_back(t);
			t.roll('E');
		}
	}
	return res;
}
//END CUT HERE

void solve_AOJ_ITP1_11_D() {
	int N; cin >> N;
	vector<Dice>d(N);
	FOR(k, 0, N) {
		FOR(i, 0, 6) {
			int val; cin >> val;
			d[k].s[i] = val;
		}
	}
	set<uLL>Se;
	Se.insert(d[0].hash());
	FOR(i, 1, N) {
		vector<Dice>dices = makeDices(d[i]);
		int flag = 0;
		FOR(j, 0, SZ(dices)) {
			flag |= (Se.count(dices[j].hash()));
		}
		if (flag) {
			cout << "No" << endl;
			return;
		}
		Se.insert(dices[i].hash());

	}
	cout << "Yes" << endl;
}


int main() {
	cin.tie(0);
	ios_base::sync_with_stdio(false);


	solve_AOJ_ITP1_11_D();


	return 0;
}