# Rotating numbers in a 2x3 grid

We have a 2x3 grid numbers like so

6 5 4
3 2 1

Four numbers in any 2x2 sub-grid can be rotated clockwise or anti-clockwise. For example

a b
c d

rotated clockwise becomes

c a
d b

Can you obtain the following grid after 5 such rotations?

1 2 3
4 5 6

First switch the parity of the $$1$$ and $$4$$, and the rest falls into place.

 654
321

625
314

365
124

326
145

136
425

123
456