Problem:
Score : 200 points

Problem Statement

It's now the season of TAKOYAKI FESTIVAL!

This year, N takoyaki (a ball-shaped food with a piece of octopus inside) will be served. The deliciousness of the i-th takoyaki is d_i.

As is commonly known, when you eat two takoyaki of deliciousness x and y together, you restore x \times y health points.

There are \frac{N \times (N - 1)}{2} ways to choose two from the N takoyaki served in the festival. For each of these choices, find the health points restored from eating the two takoyaki, then compute the sum of these \frac{N \times (N - 1)}{2} values.

Constraints

All values in input are integers.

2 \leq N \leq 50

0 \leq d_i \leq 100

Input

Input is given from Standard Input in the following format:

N
d_1 d_2 ... d_N

Output

Print the sum of the health points restored from eating two takoyaki over all possible choices of two takoyaki from the N takoyaki served.

Sample Input 1

3
3 1 2

Sample Output 1

11

There are three possible choices:

Eat the first and second takoyaki. You will restore 3 health points.

Eat the second and third takoyaki. You will restore 2 health points.

Eat the first and third takoyaki. You will restore 6 health points.

The sum of these values is 11.

Sample Input 2

7
5 0 7 8 3 3 2

Sample Output 2

312

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

public static class Program
{
    public static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        var ds = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        var sum = 0;
        for (int i = 0; i < Math.Pow(2, n); i++)
        {
            var ary = new bool[n];
            for (int j = 0; j < n; j++)
            {
                var y = (i >> j) & 1;
                ary[j] = y == 1;
            }
            if (ary.Count(x => x) != 2)
            {
                continue;
            }
            var nums = ary.Select((val, idx) => new { Value = val, Index = idx }).Where(x => x.Value).Select(x => ds[x.Index]).ToArray();
            sum += nums[0] * nums[1];
        }
        Console.WriteLine(sum);
    }
}