Problem: Problem

There are $ N $ Amidakuji with 3 vertical lines.
No matter which line you start from, the Amidakuji that ends at the starting line is considered a good Amidakuji.
You can select one or more Amidakuji and connect them vertically in any order.
Output "yes" if you can make a good Amidakuji, otherwise output "no".

There are $ w_i $ horizontal lines in the $ i $ th Amidakuji.
$ a_ {i, j} $ indicates whether the $ j $ th horizontal bar from the top of Amidakuji $ i $ extends from the central vertical line to the left or right.
If $ a_ {i, j} $ is 0, it means that it extends to the left, and if it is 1, it means that it extends to the right.

Constraints

The input satisfies the following conditions.

* $ 1 \ le N \ le 50 $
* $ 0 \ le w_i \ le 100 $
* $ a_ {i, j} $ is 0 or 1

Input

The input is given in the following format.


$ N $
$ w_1 $ $ a_ {1,1} $ $ a_ {1,2} $ ... $ a_ {1, w_1} $
$ w_2 $ $ a_ {2,1} $ $ a_ {2,2} $ ... $ a_ {2, w_2} $
...
$ w_N $ $ a_ {N, 1} $ $ a_ {N, 2} $ ... $ a_ {N, w_N} $


All inputs are given as integers.
$ N $ is given on the first line.
$ W_i $ and $ w_i $ $ a_ {i, j} $ are given on the following $ N $ line, separated by blanks.

Output

If you can make a good Amidakuji, it outputs "yes", otherwise it outputs "no".

Examples

Input

3
2 0 0
1 1
5 1 0 0 1 0


Output

yes


Input

2
1 1
1 0


Output

no

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

#define DBG cerr << '!' << endl;
#define REP(i,n) for(ll (i) = (0);(i) < (n);++i)
#define rep(i,s,g) for(ll (i) = (s);(i) < (g);++i)
#define rrep(i,s,g) for(ll (i) = (s);i >= (g);--(i))
#define PB push_back
#define MP make_pair
#define FI first
#define SE second
#define SHOW1d(v,n) {for(int W = 0;W < (n);W++)cerr << v[W] << ' ';cerr << endl << endl;}
#define SHOW2d(v,i,j) {for(int aaa = 0;aaa < i;aaa++){for(int bbb = 0;bbb < j;bbb++)cerr << v[aaa][bbb] << ' ';cerr << endl;}cerr << endl;}
#define ALL(v) v.begin(),v.end()
#define Decimal fixed<<setprecision(10)
#define INF 1000000000
#define MOD 1000000007

typedef long long ll;
typedef pair<ll,ll> P;
vector<vector<int> > v(55);

bool check(vector<int> vec){
	string str = "012";
	//cout << "!!" << endl;
	REP(i,vec.size()){
		int now = vec[i];
		REP(j,v[now].size()){
			if(v[now][j] == 0){
				swap(str[0],str[1]);
			}
			else{
				swap(str[1],str[2]);
			}
		}
		//cout << str << endl;
		if(str == "012")return true;
	}
	
	return false;
}

int main()
{
	int n;cin >> n;
	
	REP(i,n){
		int w;cin >> w;
		REP(j,w){
			int tmp;cin >> tmp;
			v[i].PB(tmp);
		}
	}
	
	if(n > 7){
		cout << "yes" << endl;
		return 0;
	}
	else
	{
		vector<int> par(n);
		REP(i,n)par[i] = i;
		do{
			if(check(par)){
				cout << "yes" << endl;
				return 0;
			}
		}while(next_permutation(ALL(par)));
	}
	
	cout << "no" << endl;
	
	return 0;
}