The Tired Painter

Ilad Rodavlas has worked as a painter all his life but is starting to get tired of his job. He brushes up, down, and up again. The same thing every day. But one day when he is about to paint a floor, divided into $N \times N$ squares, he has a brilliant idea. “Imagine if a robot could do all the work for me”, he exclaims. However, there are two problems with this idea. First, the robot can only move straight ahead, so it always paints an entire row or column with the same color. Second, Ilad cannot program. He knows, however, that you are a skilled programmer and wonders if you could help him.

Ilad has a picture that shows exactly how the floor should look in the end. The whole floor is initially unpainted. Write a program that tells the robot how to paint the floor. To avoid wasting paint, the robot must not paint the same row or column more than once.

Input

The first line contains an integer $1 \leq N \leq 9$, the number of rows and columns on the floor that the robot will paint. Following this are $N$ lines, each with $N$ characters: a dot (.) for an unpainted square, S for a black square, and V for a white square.

The floor will always be possible to paint according to the given pattern. The pattern will contain at least one painted square.

Output

First, output a string with the rows and columns the robot should paint, in order. Rows are described with the numbers 1, 2, $\dots $ from top to bottom, and columns with the letters A, B, $\dots $ from left to right.

Then output a string with the colors the robot should use each time, with the characters V for white and S for black.

Scoring

Your solution will be tested on a set of test groups, each worth a number of points. Each test group contains a set of test cases. To get the points for a test group you need to solve all test cases in the test group.

4
..S.
VVSV
..S.
..S.

2C
VS

5
VVVVV
..S.S
VVVVS
VVVVV
..S.S

C3E41
SVSVV

6
VVVVVV
VVVSVV
VVVSVV
V.VSV.
SSSSSS
V.VSV.

32EDCA51
VVVSVVSV