Practice Ascii Art with the exercise "Bouncing Barry"

Learning Opportunities

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

Ascii Art

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 E
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 ≤ 100000
1 ≤ sequence length ≤ 500

Example

Input

E S W
4 3 2

Output

####
...#
...#
.###

Solve it

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