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 PyPy3 (7.3.0) (judge verdict: Accepted)

def findProductSum(A, n): 
    array_sum = sum(A)
    array_sum_square = array_sum ** 2
    individual_square_sum = 0
    for i in range(0, n, 1): 
        individual_square_sum += A[i] * A[i] 
    return (array_sum_square -
            individual_square_sum) // 2

n = input()
arr = list(map(int, input().split()))
res = findProductSum(arr, len(arr)) % (10**9 + 7)
print(res)