$\Large \color{blue}{m}^{\color{red}{n}^{\color{darkgreen}{p}}} \times \color{red}{n}^{\color{darkgreen}{p}^{\color{blue}{m}}} \times \color{darkgreen}{p}^{\color{blue}{m}^{\color{red}{n}}} = \color{orange}3\color{blue}{m}\color{red}{n}\color{darkgreen}{p}$
Given that $$\color{blue}{m}, \color{red}{n}, \color{darkgreen}{p}$$ are positive integers that satisfy the equation above, what is the value of $$\color{blue}{m} + \color{red}{n} + \color{darkgreen}{p}$$?