Push_swap is a very simple and highly effective algorithm. You have at your disposal a list of `int` values, two stacks (`a` and `b`) and a set of instructions.
- **push_swap**, which calculates and displays on the standard output the smallest program using push_swap instruction language that sorts integer arguments received.
- **checker**, which takes integer arguments and reads instructions on the standard output. Once read, checker executes them and displays `OK` if integers are sorted. Otherwise, it will display `KO`.
As said before, you will have two stacks at your disposal. Your goal is to sort stack `a`, that will contain the `int` values received, in ascending order, using both stacks and a set of instructions.
These are the instructions that you can use to sort the stack :
-`pa` push the top first element of stack `b` to stack `a`
-`pb` push the top first element of stack `a` to stack `b`
-`sa` swap first 2 elements of stack `a`
-`sb` swap first 2 elements of stack `b`
-`ss` execute `sa` and `sb`
-`ra` rotate stack `a` (shift up all elements of stack `a` by 1, the first element becomes the last one)
- You have to write a program named push_swap, which will receive as an argument the stack a formatted as a list of integers. The first integer should be at the top of the stack.
- The program must display the smallest list of instructions possible to sort the stack `a`, with the smallest number being at the top.
- Instructions must be separated by a `\n` and nothing else.
- The goal is to sort the stack with the minimum possible number of operations.
- In case of error, you must display `Error` followed by a `\n` on the standard error. Errors are understood as: some arguments aren’t integers and/or there are duplicates.
- In case of there are no arguments the program displays nothing (0 instructions).
- You have to write a program named checker, which will get as an argument the stack `a` formatted as a list of integers. The first argument should be at the top of the stack (be careful about the order). If no argument is given, checker stops and displays nothing.
- Checker will then read instructions on the standard input, each instruction will be followed by `\n`. Once all the instructions have been read, checker will execute them on the stack received as an argument.
- If after executing those instructions, stack `a` is actually sorted and `b` is empty, then checker must display "OK" followed by a `\n` on the standard output. In every other case, checker must display "KO" followed by a `\n` on the standard output.
- In case of error, you must display Error followed by a `\n` on the standard error. Errors include for example: some arguments are not integers, there are duplicates, an instruction don’t exist and/or is incorrectly formatted.
- In case of there are no arguments the program displays nothing.
