On a chessboard consisting of n × n cells, several of them are cut. Find the path of minimum length for a Knight from one cell to another. The Knight can’t go through cut cells.

Input

The first row is set to the number n (2 ≤ n ≤ 50). Each of the next n lines contains n symbols. The symbol #denotes the cut cell, the point is not a cut cell, and the symbol @ denotes the initial and final cell of the Knight's path (the chessboard contains two such characters).

Output

If the path can not be constructed, print "Impossible". Otherwise, print the same map as the input, but check all Knight intermediate positions with the symbol @.