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
$N = (int) trim(fgets(STDIN));
$A = trim(fgets(STDIN));
$A_arr = explode(" ", $A);

$result = 0;
for ($i=1; $i <= $N - 1; $i++) {
  for ($j=$i+1; $j <= $N; $j++) {
    $result += $A_arr[$i - 1] * $A_arr[$j - 1];
  }
}
echo $result % 1000000007;