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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php
fscanf(STDIN, "%d", $n);
$input = explode(' ',trim(fgets(STDIN)));

$mod = 10**9 + 7;
$ans = 0;
foreach ($input as $key => $value) {
    for ($i=1; $i <= $n ; $i++) {
        $num = $key+$i;
        if ($num < $n) {
            $result = $value * $input[$num] % $mod;
            $ans += $result;
        }
    }
}
echo $ans % $mod;