Practice Coding with the exercise "Hourglass"

Statement

Goal

You will be given the ASCII representation of a hourglass followed by a number of seconds N. You have to output the representation of the hourglass exactly as it should look like after N seconds have passed.

The hourglass will be received as input of 23 lines composing its body . (Check the example)

The following apply:

- the capacity of the hourglass is 100 grains of sand
- an 'o' is the representation of one grain of sand which is 1 second
- "7 seconds have passed" means 7 o's have moved from the top half of the hourglass to the bottom half

There are rules as to which grain of sand is the next one to leave the top half and to where it should be placed in the bottom half.

TOP HALF

The sand empties from the middle of the hourglass to the sides 1 grain at a time.
Let's consider a full TOP HALF. The order grains are being removed is as follows:
1. middle grain from topmost line that's not missing any grains
2. 4 middlemost grains from all lines from top to bottom that are missing grains until a line that's not missing any grains (don't touch that line)
3. Repeat from 1
The pattern for removing consecutive grains on the same horizontal line is as follows:

ooooooo -> ooo ooo -> ooo  oo -> oo   oo -> oo    o -> o     o

o - the grain that will be removed next

BOTTOM HALF

The sand fills this half from the middle of the hourglass to the sides 1 grain at a time.
Let's consider an empty BOTTOM HALF. First 10 grains make up a vertical trail from the middle of the hourglass until they reach the bottom. (check the example) The order grains are being inserted after the trail is as follows:
1. 2 middlemost grains on the bottom line
2. 2 middlemost grains on the bottom line going up adding 2 middlemost grains on every line until a triangle is formed with it's tip being a grain from the vertical trail
3. Repeat from 2
The pattern for inserting consecutive grains on the same horizontal line is as follows:

o -> oo -> ooo -> oooo -> ooooo -> ooooo

Important notes:
- every line from your hourglass should end with either /, X, \, +. Watch out for leftover spaces.
- only the output must respect the above rules, meaning that the input can have random placed grains
- if the amount of grains in the hourglass received from the input is not equal to 100 the program should output the message BROKEN HOURGLASS instead of a hourglass
- N can be greater than the amount of grains in the TOP HALF which means that the sand will fill the BOTTOM HALF completely before N seconds. In that case the output should still be a normal BOTTOM HALF full hourglass.

Suggestion: draw a full top hourglass in notepad and apply the rules until you understand them.

To finish with a quote:
The more sand that has escaped from the hourglass of our life, the clearer we should see through it. Good luck!

Input

First 23 lines : 23 strings hLine composing the body of the hourglass
Next line : An integer N representing the number of seconds to pass

Output

The representation of the hourglass as given in the input, modified to resemble the N seconds that have passed or the message BROKEN HOURGLASS

Constraints

0 ≤ N ≤ 100

Example

Input

+=====================+
 \ooooooooooooooooooo/
  \ooooooooooooooooo/
   \ooooooooooooooo/
    \ooooooooooooo/
     \ooooooooooo/
      \ooooooooo/
       \ooooooo/
        \ooooo/
         \ooo/
          \o/
           X
          / \
         /   \
        /     \
       /       \
      /         \
     /           \
    /             \
   /               \
  /                 \
 /                   \
+=====================+
15

Output

+=====================+
 \ooooo         ooooo/
  \oooooo     oooooo/
   \ooooooo ooooooo/
    \ooooooooooooo/
     \ooooooooooo/
      \ooooooooo/
       \ooooooo/
        \ooooo/
         \ooo/
          \o/
           X
          /o\
         / o \
        /  o  \
       /   o   \
      /    o    \
     /     o     \
    /      o      \
   /       o       \
  /        oo       \
 /       ooooo       \
+=====================+

Solve it

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