Ghost Legs

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

inputFormat

outputFormat

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

样例

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

yes