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;
void END(){
  cout<<"yes"<<endl;
  exit(0);
}
int main(){
  int n,m,x;
  cin>>n;
  vector<vector<int> >v(n);
  if(n>4)END();
  for(int i=0;i<n;i++){
    for(int j=0;j<3;j++) v[i].push_back(j);
    cin>>m;
    while(m--){
      cin>>x;
      if(x)swap(v[i][1],v[i][2]);
      else swap(v[i][0],v[i][1]);
    }
  }
  sort(v.begin(),v.end());
  do{
    for(int i=0;i<n;i++){
      int a[]={1,2,3},tmp[3];
      for(int j=0;j<=i;j++){
        for(int k=0;k<3;k++)tmp[k]=a[k];
        for(int k=0;k<3;k++)a[k]=tmp[v[j][k]];
      }
      if(a[0]==1&&a[1]==2&&a[2]==3)END();
    }
  }while(next_permutation(v.begin(),v.end()));
  cout<<"no"<<endl;
}