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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::*;
use proconio::{input, fastout, marker::*};

#[fastout]
fn main() {
  input!{
      n: u64,
      a: [u64;n]
  }
  let mut s:u64 = a.iter().sum();
  let mut ans:u64 = 0;
  let MOD = 1_000_000_007;
  for i in a {
      s -= i;
      ans += ((s%MOD)*(i%MOD))%MOD;
      ans %= MOD;
  }
  println!("{}",ans);
}