Competitions

The way a Knight

Given 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 (2n50). Each of the next n lines contains n symbols. The symbol # denotes the cut cell, the point - not cut cell, 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 display the same map as the input, but check all Knight intermediate positions with symbol @.

Time limit 1 second
Memory limit 122.17 MiB
Input example #1
5
.....
.@@..
.....
.....
.....

Output example #1
.....
.@@..
...@.
.@...
.....

Input example #2
5
@..@.
..##.
.....
.....
.....

Output example #2
@..@.
..##.
.@@..
...@.
.@...

Input example #3
5
@....
..#..
.#...
.....
....@

Output example #3
Impossible