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

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
def amida():
	line = list(map(int, input().split()))[1:]
	res = [0, 1, 2]
	for i in line:
		if i:
			(res[1], res[2]) = (res[2], res[1])
		else:
			(res[0], res[1]) = (res[1], res[0])
	return res

def func(x, line, flag):
	if line == [0, 1, 2] and flag:
		return True
	for i in range(27):
		if x[i] == 0:
			continue
		swaps = tolist(i)
		x[i] -= 1
		res = func(x, [line[swaps[0]], line[swaps[1]], line[swaps[2]]], True)
		x[i] += 1
		if res:
			return True
	return False
n = int(input())
if n >= 7:
	print('yes')
	exit()
amidas = [amida() for _ in range(n)]
toint = lambda x: x[0] * 9 + x[1] * 3 + x[2]
tolist = lambda x: [x // 9, x % 9 // 3, x % 3]
aa = [0 for _ in range(27)]
for i in amidas:
	aa[toint(i)] += 1
flag = False
for i in range(27):
	if aa[i] == 0:
		continue
	line = [0, 1, 2]
	for j in range(aa[i]):
		swaps = tolist(i)
		line = [line[swaps[0]], line[swaps[1]], line[swaps[2]]]
		if line == [0, 1, 2]:
			flag = True
			break
if flag:
	print('yes')
	exit()
if func(aa, [0, 1, 2], False):
	print('yes')
	exit()
print('no')


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)
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')


N = int(input())
SET = [0, 0, 0, 0, 0, 0]
judge = [[2, 1, 3], [1, 3, 2], [3, 2, 1], [2, 3, 1], [3, 1, 2], [1, 2, 3]]
for _ in range(0, N):
	ID = [1, 2, 3]
	amida = [int(x) for x in input().split()]
	for j in range(1, len(amida)):
		if amida[j] == 0:
			(ID[0], ID[1]) = (ID[1], ID[0])
		elif amida[j] == 1:
			(ID[1], ID[2]) = (ID[2], ID[1])
	for i in range(0, len(judge)):
		if ID == judge[i]:
			SET[i] += 1
if SET[5] > 0 or SET[0] > 1 or SET[1] > 1 or (SET[2] > 1) or (SET[0] > 0 and SET[1] > 0 and (SET[4] > 0)) or (SET[0] > 0 and SET[2] > 0 and (SET[4] > 0)) or (SET[0] > 0 and SET[2] > 0 and (SET[4] > 0)) or (SET[0] > 0 and SET[1] > 0 and (SET[3] > 0)) or (SET[0] > 0 and SET[2] > 0 and (SET[3] > 0)) or (SET[1] > 0 and SET[2] > 0 and (SET[4] > 0)) or (SET[3] > 0 and SET[4] > 0) or (SET[3] > 2) or (SET[4] > 2):
	print('yes')
else:
	print('no')