Practice Arrays and Run-length encoding with the exercise "Binary image"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Arrays

Statement

Goal

You are going to write a simple program to decode some arrays of data into a black-and-write graphic.

The graphic is composed of n lines of black and white pixels. We use . to represent a white pixel; O to represent a black pixel.

For example, here is one line of graphic
....OOO.

We shall encode it into an array 4 3 1
because it starts with 4 whites, then 3 blacks, then 1 white.
We assume most lines shall start with white.

When there is a line starting with black, we add 0 at the beginning of the encoded data, to say there is no white pixel before the first black pixel.
For example
OO.OOOOO
will be encoded into 0 2 1 5.

You must output INVALID if the graphic is not rectangular (this doesn't mean the input lines should be the same length, but the outputs lines should be).

In this puzzle, you will be given n lines of encoded data.
You are going to decode it into a graphic.

Input

First line : Number n of rows in the graphic (integer)
n next lines : An array of integers representing the encoded nth line of the graphic

Output

If the grid is not a rectangle : INVALID
Otherwise : n lines of the grid (equal length), each pixel represented by ./O, no spaces

Constraints

n < 200

Example

Input

Output

.OOO..O
.OOO..O
.OOO..O
.OOO..O

Solve it

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