Added solution for Project Euler problem 77 (#3132)

* Added solution for Project Euler problem 77.

* Update docstrings, doctest, type annotations and 0-padding in directory name. Reference: #3256

* Implemented lru_cache, better type hints, more doctests for problem 77

* updating DIRECTORY.md

* updating DIRECTORY.md

* Added solution for Project Euler problem 77. Fixes: 2695

* Update docstrings, doctest, type annotations and 0-padding in directory name. Reference: #3256

* Implemented lru_cache, better type hints, more doctests for problem 77

* better variable names

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