You are given a box with eight holes labelled   A-to-H,   connected by fifteen straight lines in the pattern as shown below:

             A   B
            /│\ /│\
           / │ X │ \
          /  │/ \│  \
         C───D───E───F
          \  │\ /│  /
           \ │ X │ /
            \│/ \│/
             G   H

You are also given eight pegs numbered   1-to-8.



Objective

Place the eight pegs in the holes so that the (absolute) difference between any two numbers connected by any line is greater than one.



Example

In this attempt:

             4   7
            /│\ /│\
           / │ X │ \
          /  │/ \│  \
         8───1───6───2
          \  │\ /│  /
           \ │ X │ /
            \│/ \│/
             3   5

Note that   7   and   6   are connected and have a difference of   1,   so it is   not   a solution.



Task
Produce and show here   one   solution to the puzzle.



Related tasks

   A* search algorithm
   Solve a Holy Knight's tour
   Knight's tour
   N-queens problem
   Solve a Hidato puzzle
   Solve a Holy Knight's tour
   Solve a Hopido puzzle
   Solve a Numbrix puzzle
   4-rings or 4-squares puzzle


See also
No Connection Puzzle (youtube).




holes=:;:'A B C D E F G H'
 
connections=:".;._2]0 :0
 holes e.;:'C D E'          NB. A
 holes e.;:'D E F'          NB. B
 holes e.;:'A D G'          NB. C
 holes e.;:'A B C E G H'    NB. D
 holes e.;:'A B D F G H'    NB. E
 holes e.;:'B E H'          NB. F
 holes e.;:'C D E'          NB. G
 holes e.;:'D E F'          NB. H
)
assert (-:|:) connections NB. catch typos
 
pegs=: 1+(A.&i.~ !)8
 
attempt=: [: <./@(-.&0)@,@:| connections * -/~
 
 
box=:0 :0
        A   B
       /|\ /|\
      / | X | \
     /  |/ \|  \
    C - D - E - F
     \  |\ /|  /
      \ | X | /
       \|/ \|/
        G   H
)
 
disp=:verb define
  rplc&(,holes;&":&>y) box
)