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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

class Main {
  public static void main(String[] args) {

    var m = 1000000000 + 7;

    var sc = new Scanner(System.in);

    var n = sc.nextInt();
    var a = new int[n];
    for (int i = 0; i < n; i++) {
      a[i] = sc.nextInt() % m;
    }

    long answer = 0;
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        answer = (answer + (long)a[i] * a[j] % m) % m;
      }
    }

    System.out.println(answer);

  }
}