ELMO 2016 Problem 1

Cookie Monster says a positive integer $n$ is $crunchy$ if there exist $2n$ real numbers $x_1,x_2,\ldots,x_{2n}$ , not all equal, such that the sum of any $n$ of the $x_i$ 's is equal to the product of the other $n$ of the $x_i$ 's. Help Cookie Monster determine all crunchy integers.

Yannick Yao