Problem C
Diagonals
Diagonals is a pencil puzzle which is played on a square grid. The player must draw a diagonal line corner to corner in every cell in the grid, either top left to bottom right, or bottom left to top right. There are two constraints:

Some intersections of gridlines have a number from $0$ to $4$ inclusive on them, which is the exact number of diagonals that must touch that point.

No set of diagonals may form a loop of any size or shape.
The following is a $5\! \times \! 5$ example, with its unique solution:
Given the numbers at the intersections of a grid, solve the puzzle.
Input
The first line of input contains an integer $n$ ($1 \le n \le 8$), which is the size of the grid.
Each of the next $n+1$ lines contains a string $s$ ($s=n+1, s \in \{ \texttt{0},\texttt{1},\texttt{2},\texttt{3},\texttt{4},\texttt{+}\} ^*$). These are the intersections of the grid, with ‘+’ indicating that there is no number at that intersection.
The input data will be such that the puzzle has exactly one solution.
Output
Output exactly $n$ lines, each with exactly $n$ characters, representing the solution to the puzzle. Each character must be either ‘/’ or ‘\’.
Note that Sample 1 corresponds to the example in the problem description.
Sample Input 1  Sample Output 1 

5 +1+2++ 1++11+ +3+2++ 02+++1 ++3+1+ +1+++1 
\\/\\ \/\\/ \\\\\ ////\ //\\\ 
Sample Input 2  Sample Output 2 

3 ++++ +1+1 +31+ +0+0 
/\/ /// /\/ 
Sample Input 3  Sample Output 3 

4 +++++ +3++2 ++3++ +3+3+ ++2+0 
\//\ \\// \\\/ /\// 