https://ja.wikipedia.org/wiki/%E3%82%A2%E3%83%83%E3%82%AB%E3%83%BC%E3%83%9E%E3%83%B3%E9%96%A2%E6%95%B0
memo化: https://ideone.com/OJjfxv
非memo化: https://ideone.com/JMmj6U