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: Wrong Answer)

// -*- coding:utf-8-unix -*-


use proconio::fastout;

#[fastout]
fn main() {
   
    let n = 4;
    let a = [999999999,695902862,6437808753,678889467];

    let mut ans = 0;
    let mut start = 1;
    let mut mass = 0;

    const  MOD: usize = 1000000000 + 7;

    for elem in &a[..n-1] {
        mass += elem;
      
        ans += mass * &a[start];
        ans %= MOD; 
        mass %= MOD;
        start += 1;
    }; 
    

    let mut ans = 0;
    let mut start = 1;
    let mut mass = 0;


    for elem in &a[..n-1] {
        mass += elem;
      
        ans += mass * &a[start];
        start += 1;
    };

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


    
    
}