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 X 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 ≤ n ≤ 8), which is the size of the grid.

Each of the next n+1 lines contains a string s (|s|=n+1, s ∈ {0, 1, 2, 3,4, +}^*). 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.

5
+1+2++
1++11+
+3+2++
02+++1
++3+1+
+1+++1

\\/\\
\/\\/
\\\\\
////\
//\\\

3
++++
+1+1
+31+
+0+0

/\/
///
/\/

4
+++++
+3++2
++3++
+3+3+
++2+0

\//\
\\//
\\\/
/\//