Appleman and Easy Task

Toastman came up with a very easy task. He gives it to Appleman, but Appleman doesn't know how to solve it. Can you help him?

Given a n × n checkerboard. Each cell of the board has either character 'x', or character 'o'. Is it true that each cell of the board has even number of adjacent cells with 'o'? Two cells of the board are adjacent if they share a side.

Input

The first line contains an integer n (1 ≤ n ≤ 100). Then n lines follow containing the description of the checkerboard. Each of them contains n characters (either 'x' or 'o') without spaces.

Output

Print "YES" or "NO" (without the quotes) depending on the answer to the problem.

Examples

Input

3 xxo xox oxx

Output

YES

Input

4 xxxo xoxo oxox xxxx

Output

NO

inputFormat

Input

The first line contains an integer n (1 ≤ n ≤ 100). Then n lines follow containing the description of the checkerboard. Each of them contains n characters (either 'x' or 'o') without spaces.

outputFormat

Output

Print "YES" or "NO" (without the quotes) depending on the answer to the problem.

Examples

Input

3 xxo xox oxx

Output

YES

Input

4 xxxo xoxo oxox xxxx

Output

NO

样例

3
xxo
xox
oxx

YES

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