Problem:
Score : 300 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

Find the sum of A_i \times A_j over all pairs (i,j) such that 1\leq i < j \leq N, modulo (10^9+7).

Constraints

2 \leq N \leq 2\times 10^5

0 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

Print \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} A_i A_j, modulo (10^9+7).

Sample Input 1

3
1 2 3

Sample Output 1

11

We have 1 \times 2 + 1 \times 3 + 2 \times 3 = 11.

Sample Input 2

4
141421356 17320508 22360679 244949

Sample Output 2

437235829

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::{fastout, input};

const MOD: u64 = 1_000_000_007;

#[fastout]
fn main() {
    input! {
        n: usize,
        a: [u64; n],
    }

    let mut ans = 0;
    let mut sum: u64 = a.iter().sum();

    for i in a {
        sum -= i;
        ans += (sum % MOD) * (i % MOD) % MOD;
        ans %= MOD;
    }

    println!("{}", ans);
}