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.

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 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.