Laziness

For some reason, Hyunwoo has ended up needing $n$ iron bars of lengths $a_1, \dots, a_n$. But all he had was a single iron bar of length $a_1 + \cdots + a_n$. Hyunwoo will cut this bar himself to make the $n$ bars he originally needed. Cutting a bar of length $x+y$ into two bars of lengths $x$ and $y$ costs $xy$, the product of the lengths of the two bars he wants to make. Hyunwoo wants to cut this bar at minimum cost to obtain the $n$ bars of lengths $a_1, \dots, a_n$.

However, Hyunwoo is not sure how much this cost will be. So he has offered to raise your Code Jam contest score by 30 points if you write a program that computes the minimum cost of cutting the bar. How about it?

The first line gives the integer $n$, the number of iron bars Hyunwoo wants. ($1 \le n \le 500{,}000$)

The second line gives the integers $a_1, \dots, a_n$, the lengths of the iron bars Hyunwoo wants. ($1 \le a_i \le 101$)

Print the minimum cost for Hyunwoo to obtain the $n$ iron bars he needs.