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 Julia (1.4.0) (judge verdict: Accepted)

function main()
  
  n = parse(Int, readline())
  A = parse.(Int, split(readline()))
  
  A_sum = sum(A)
  A_sum %= 10^9+7
  
  ans = 0
  for i in 1:n
    A_sum -= A[i]
    if A_sum < 0
      A_sum += 10^9+7
    end
    ans += A[i]*A_sum
    ans %= 10^9+7
  end
  
  println(ans)
  
end

main()