Now lets simplify this by computing the permutation.

so lets immagine sending 1 in on the right ...

1 goes through (2,4) unchanaged.

1 goes into (1,3) and comes out 3

3 goes into (1,3,4) and comes out 4

so 1 goes to 4 (1,4

Now lets send 4 in

4 goes into (2,4) and comes out 2

2 goes into (1,3) and is unchanged.

2 goes into (1,3,4) and is unchanges

so 4 goes to 2 (1,4,2

Now lets send 2 in

2 goes into (2,4) and comes out 4

4 goes into (1,3) and is unchanged

4 goes into (1,3,4) and comes out 1

so 2 goes to 1 (1,4,2)

Now the only number we didn't check in are chain is 3.

if you check it 3 goes to 3.

so we end up with