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 Fortran (GNU Fortran 9.2.1) (judge verdict: Time Limit Exceeded)

program sum_of_product
    implicit none
    integer(16) n, i, y,ans,x,z,j
    integer(16),allocatable :: a(:)

    read *, n
    allocate(a(n))
    read *, a
    y=0
    x=0
    z=0
    j=0

    if(2<=n .or. n<=200000)then
        do i=1,n
            if(0<=a(i) .or. a(i)<=1000000000)then
                x=x+a(i)
                y=sum(a)-x
                z=y*a(i)
                j=j+z
            end if
        end do
    end if
    ans=modulo(j,1000000007)
    print *,ans
end program sum_of_product