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: Runtime Error)

use proconio::input;

const MOD: i64 = 1000000007;


fn main() {
    input! {
        n: usize,
        an: [i64; n],
    }

    let mut j_sum: i64 = 0;
    for a in an.iter() {
        j_sum += a;
        j_sum %= MOD;
        if j_sum < 0 {
            j_sum += MOD;
        }
    }

    let mut res = 0;
    for a in an.iter() {
        j_sum -= a;
        res += a * j_sum % MOD;
        res %= MOD;
        if res < 0 {
            res += MOD;
        }
    }
    assert_eq!(j_sum, 0);
    println!("{:?}", res);
}