Gokigen Naname is a Japanese puzzle game played on
a square grid in which numbers in circles appear at some of the
intersections on the grid.
The objective is to draw diagonal lines in each cell of the
grid, such that the number in each circle equals the number of
lines extending from that circle. Additionally, it is forbidden
for the diagonal lines to form an enclosed loop.
Figure 1: The first figure shows the start position
of a puzzle. The second figure shows the solution to the
same puzzle. A Gokigen Naname puzzle always has
exactly one solution.
The first line of the input contains a single integer
$n$ ($2 \le n \le 7$), the number of cells
along each of the sides in the square grid. Then follow
$n + 1$ lines containing
the contents of the intersections of the grid cells. Each such
line will contain a string of $n
+ 1$ characters, either a digit between 0 and 4,
inclusive, or a period (’.’) indicating that there is no number
at this intersection (arbitrarily many lines may connect to
The output should contain $n$ lines, each line containing
exactly $n$ characters.
Each character should either be a slash or a backslash,
denoting how the corresponding grid cell is filled.
|Sample Input 1
||Sample Output 1
|Sample Input 2
||Sample Output 2