Beautification of array

Chef has an array and he also likes beautiful things. So he wants to make his array as beautiful as possible. He defines the $Beauty$ of his array as the sum of all pairwise products of the elements of the array. $$ Beauty([A_1, A_2, \dots, A_N]) = \displaystyle\sum\limits_{i=1}^N\displaystyle\sum\limits_{j=i+1}^N A[i] \cdot A[j] $$ To make his array more beautiful, he can do the following ope