Please write a Reverse Polish Notation Analyzer code in Rust. Certain RPN programs are ill-formed, like the following which attempts to perform an addition operation with too few integers on the stack: You'll implement a program that analyzes an RPN program to determine (1) whether it is well formed (won't produce errors when run) and (2) if it is well formed, how large a stack the program will require to run.

In general, RPN programs may require stacks that scale with the size of the program being executed. For example:

1 2 3 4 5 6 7 8 ... N + ... + + + + + + + done 

pushes a bunch of integers, from 1 to N for some large N, then repeatedly adds the results until only the sum of all the values 1 to N is left on the stack.

• -1 if the RPL program on stdin was invalid according to the grammar; or
• N if the the RPL program on stdin was valid, where N is the maximum number of stack slots required total, in both the main and auxiliary stacks, to execute the program.

The following are input and output to run

Examples

Program	Result	Reason
1 2 3 done	3
1 2 3	-1	Missing done
1 2 + 3 + 4 + 5 + done	2
1 2 3 4 5 + + + + done	5
1 2 + save 3 restore + done	3	Main stack 2 + auxiliary stack 1
1 2 + done 3 4 5 done	2	All code after the first done is ignored