Goal
Given a shape in an H x W pixel grid, where # represents a part of the shape, and . represents an empty space, you need to output the outline of the shape as a sequence of vertices. Start from the top-leftmost point of first line of text and follow the shape's boundary in a clockwise direction. Multiply vertex X and Y with pixel size S to get the final coordinates.
The top-leftmost vertex of the grid is (0, 0), with the X-coordinate increasing towards the right and Y-coordinate increasing downwards. A single square represented in the input is made of S units of length.
Every shape can be drown with a single stroke. There are no hollow spaces or diagonally touching squares (forming the shape), only one path can be followed.
Input
Line 1: H height of the pixel art grid
Line 2: W width of the pixel art grid
Line 3: S pixel size
Next H lines: pixel art line
Output
N lines: Two space-separated integers, representing the X and Y coordinates of a vertex of the shape's outline (and there are N vertices in total).
Constraints
2 ≤ H ≤ 19
2 ≤ W ≤ 32
4 ≤ N ≤ 140
Example
Output
10 0
20 0
20 20
0 20
0 10
10 10
