Find all positive integers $ n $ with the following property: It is possible to fill a $ n \times n $ chessboard with one of arrows $ \uparrow, \downarrow, \leftarrow, \rightarrow $ such that 

1. Start from any grid, if we follows the arrows, then we will eventually go back to the start point.

2. For every row, except the first and the last, the number of $ \uparrow $ and the number of $ \downarrow $ are the same. 

3. For every column, except the first and the last, the number of $ \leftarrow $ and the number of $ \rightarrow $ are the same.