There is a grid with $N$ rows and $N$ columns. The cell in the $i$-th row from the top ($1 \le i \le N$) and the $j$-th column from the left ($1 \le j \le N$) is denoted as cell $(i, j)$. A character $C_{i,j}$ is written in cell $(i, j)$, where $C_{i,j}$ is either o or x.

Output Yes if there exists a row in which all characters are the same, or a column in which all characters are the same; otherwise, output No.

Constraints

• $1 \le N \le 100$.
• $C_{i,j}$ is either o or x ($1 \le i \le N$, $1 \le j \le N$).
• $N$ is an integer.

Input

The input is given in the following format:

N
C_{1,1} C_{1,2} ... C_{1,N}
C_{2,1} C_{2,2} ... C_{2,N}
...
C_{N,1} C_{N,2} ... C_{N,N}

Output

Output Yes if there exists a row in which all characters are the same, or a column in which all characters are the same; otherwise, output No.

Do not output anything other than the answer. (Do not output prompt sentences or anything similar.)

Examples

Input 1

3
o x x
o o x
o x o

Output 1

Yes

Note 1

$C_{1,1} =$ o, $C_{2,1} =$ o, $C_{3,1} =$ o, so all characters in the $1$-st column are o. Therefore, output Yes.

Input 2

4
o x x x
x o x x
x x o x
x x x o

Output 2

No

Note 2

• There is no row in which all characters are the same.
• There is no column in which all characters are the same.

Therefore, output No.

Input 3

6
x x o o x x
x o x x o x
o x x x x o
o x x x x o
x o x x o x
x x o o x x

Output 3

No

Note 3

• There is no row in which all characters are the same.
• There is no column in which all characters are the same.

Therefore, output No.

Input 4

10
o x o o o x o x o x
o o x o o x o o o x
x o o x o o o x x x
o o o x o o x o x x
o o o o o o o x o x
x x x x x x x x x x
o o o x o o o o o x
o o o x o o o o o x
o o o x o o x x o x
o x o o o o x o o x

Output 4

Yes

Note 4

In the $10$-th column and the $6$-th row, all characters are the same in each, so output Yes.