Sum of Pairwise Products

Given n integers \(a_{1}, a_{2}, \dots, a_{n}\), your task is to compute the sum of the product of every pair, i.e.,

\[ S = a_{1} \cdot a_{2} + a_{1} \cdot a_{3} + \cdots + a_{1} \cdot a_{n} + a_{2} \cdot a_{3} + \cdots + a_{n-2} \cdot a_{n-1} + a_{n-2} \cdot a_{n} + a_{n-1} \cdot a_{n} \]

An efficient way to solve this problem is to use the formula:

\[ S = \frac{(a_{1} + a_{2} + \cdots + a_{n})^2 - (a_{1}^2 + a_{2}^2 + \cdots + a_{n}^2)}{2} \]

inputFormat

The first line of input contains an integer n, the number of integers.

The second line contains n integers separated by spaces.

outputFormat

Output a single integer: the sum of the product of every pair.

sample

3
1 2 3

11