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

Statement

 Goal

Barry the bouncing bunny is a bit braindead. Barry mindlessly jumps around on an infinitely large square grid, comprising tiles that initially display the . character. Each time Barry lands on a tile, the tile toggles between displaying . and #.

Barry's bouncing behavior is described with a space-separated sequence of directions d_1 d_2 d_3... followed by an index-matched integer sequence for bounce count b_1 b_2 b_3... Directions are any of the four cardinal directions NSEW. Bounce count describes how many tiles Barry bounces forward in a straight line. Turning does not count as a bounce.

After Barry has finished his bouncing business, print the appearance of the floor, cropped to the smallest rectangle that includes all #'s.

For example, the input
E S W
4 3 1

would produce the floor as shown:
........
..####..
.....#..
.....#..
....##..
........

but this should be printed instead:
####
...#
...#
..##

If no tiles show # at the end of Barry's bouncing, simply print . instead.
Input
Line 1: A string containing a space-separated sequence of characters NSEW representing bouncing direction
Line 2: A string containing a space-separated sequence of integers representing bounce count
Output
A map of the floor, consisting of characters # and .
Constraints
1 ≤ bounces per action ≤ 30000
1 ≤ sequence length ≤ 500
Example
Input
E S W
4 3 2
Output
####
...#
...#
.###

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