A regular 12 -gon is inscribed in a circle of radius 12 . The sum of the lengths of all sides and diagonals of the 12 -gon can be written in the form

a+b \sqrt{2}+c \sqrt{3}+d \sqrt{6}

where a, b, c, and d are positive integers. Find a+b+c+d.

A regular 12 -gon is inscribed in a circle of radius 12 . The sum of the lengths of all sides and diagonals of the 12 -gon can be written in the form

a+b \sqrt{2}+c \sqrt{3}+d \sqrt{6}

where a, b, c, and d are positive integers. Find a+b+c+d.