sort array of 3 keys while minimizing the total cost

i ve asked the same question 6 months ago but havent really understood how to solve this yet

suppose that we have an array of size n where n <=10 and the keys are 1,2,3

if n = 3 then

we want to find the min cost in order to sort it in an ascending order

one way would be the following

Code:

`2 1 3`

2 3 1

1 3 2

1 2 3

with a total cost of 3

another way would be the following

with a total cost of 1

but if we have a bigger number of n for example n = 5 the problem gets harder

etc

i ve tried many sorting algorithms, one that suits the problem is counting sort, but that hasnt helped me at all

can anyone please help me with hints? thanks