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 Rust (1.15.1) (judge verdict: Wrong Answer)

// Template from https://techracho.bpsinc.jp/jhonda/2019_08_05/78537

// input macro for competive-programming from https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };

    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, bytes) => {
        read_value!($iter, String).into_bytes()
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

fn main() {
    use std::io::Read;
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();

    println!("{}", solve(&s));
}

macro_rules! test {
    ($($input:expr => $output:expr),* $(,)*) => {
        #[test]
        fn solve_test() {
            $(
                assert_eq!(solve($input), $output);
            )*
        }
    };
}

test! {
r#"3
3 1 2"# => r#"11"#,

r#"7
5 0 7 8 3 3 2"# => r#"312"#,
}

fn solve(src: &str) -> String {
    input! {
        source = src,
        n: usize,
        d: [u64; n],
    }

    let total = (0..(1 << n))
        .map(|ix| (0..n).filter(|j| ix & (1 << j) > 0).collect::<Vec<usize>>())
        .filter(|ix| ix.len() == 2)
        .map(|ix| ix.iter().map(|&i| d[i]).collect::<Vec<u64>>())
        .map(|ix| ix.iter().product::<u64>())
        .sum::<u64>();


    // println!("{}", total);
    // println!("{:?}", (0..(1 << n))
    //                 .map(|ix| (0..n).filter(|j| ix & (1 << j) > 0).collect::<Vec<usize>>())
    //                 .filter(|ix| ix.len() == 2)
    //                 .map(|ix| ix.iter().map(|&i| d[i]).collect::<Vec<usize>>())
    //                 .collect::<Vec<Vec<usize>>>()
    //         );
    // println!("{:?}", (0..(1 << n))
    //                 .map(|ix| (0..n).filter(|j| ix & (1 << j) > 0).collect::<Vec<usize>>())
    //                 .filter(|ix| ix.len() == 2)
    //                 .map(|ix| ix.iter().map(|&i| d[i]).collect::<Vec<usize>>())
    //                 .map(|ix| ix.iter().product::<usize>())
    //                 .collect::<Vec<usize>>()
    //         );

    total.to_string()
}