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 PYTHON3):

Solution:
N = int(input())
C = [0]*6
S = [[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0, 1], [2, 1, 0]]
L = [1, 2, 2, 3, 3, 2]
P = []
init = [0, 1, 2]
for i in range(N):
    w, *A = map(int, input().split())
    state = init[:]
    for a in A:
        if a:
            state[1], state[2] = state[2], state[1]
        else:
            state[0], state[1] = state[1], state[0]
    j = S.index(state)
    C[j] += 1
    if C[j] >= L[j]:
        print('yes')
        exit(0)
    P.append(state)

# case: "L <= [0, 1, 1, 2, 2, 1]"
from itertools import permutations
for p in permutations(P):
    s = init[:]
    for q in p:
        s[0], s[1], s[2] = s[q[0]], s[q[1]], s[q[2]]
    if s == init:
        print('yes')
        exit(0)
print('no')