]= rightmost point of a sorted subgroup
  [= leftmost point of a sorted subgroup
  | indicate the ends of the block_exchange points
  ^ indicates the center about which the exchange is made
  
 [ 1 7 15 32] [3 17 54 63][27 35 59 60][11 23 24 29]
 [ 1 |7 15 32]^[3 17| 54 63][27 35 59 60][11 23 24 29]
 [ 1 |7 15 32]^[3 |17 54 63][27 35 59 60][11 23 24 29]
 [ 1 3 ][7 15| 32]^[17 |54 63][27 35 59 60][11 23 24 29]
 [ 1 3 7 15 17| 32 54 63]^[27| 35 59 60][11 23 24 29]
 [ 1 3 7 15 17  27 32 |54 63]^[35| 59 60][11 23 24 29]
 [ 1 3 7 15 17  27 32 35 54 |63]^[59 60]|[11 23 24 29]
 [ 1 3 7 |15 17  27 32 35 54 59 60 63]^[11| 23 24 29]
 [ 1 3 7 11 15 17 |27 32 35 54 59 60 63]^[23 24| 29]
 [ 1 3 7 11 15 17 23 24 27| 32 35 54 59 60 63]^[29]|
 [ 1 3 7 11 15 17 23 24 27 29 32 35 54 59 60 63]