Switchboard

Can you sort out the mess?

Run 3

Input

A B C D E
| | | | |
 \|/  | |
  X    X
 /|\  | |
| | | | |
| | | | |
 X   \|/
| |   X
| |  /|\
| | | | |
|  X   X
| | | | |

Expected Output

B D C A E