Memory

There are $N$ memory modules that can function only in pairs. Some of the modules are defective, while others are functioning properly. By inserting two modules into the computer and running a test program, you receive one of the following two results:

• Both modules are functioning properly;

• At least one module is defective (or both), but it is not known which one.

After testing any pair of modules, you may choose any next pair to test.

Determine the minimum number of tests required in the worst case to identify exactly which modules are functioning properly, or to prove that it is impossible to determine the set of functioning modules.