Let A B C D E F be an equiangular hexagon. The lines A B, C D, and E F determine a triangle with area 192 \sqrt{3}, and the lines B C, D E, and F A determine a triangle with area 324 \sqrt{3}. The perimeter of hexagon A B C D E F can be expressed as m+n \sqrt{p}, where m, n, and p are positive integers and p is not divisible by the square of any prime. What is m+n+p ?

**Answer Choices**

A. 47

B. 52

C. 55

D. 58

E. 63