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: Wrong Answer)

program C177
    implicit none
    integer(8) :: N
    integer(8), allocatable, dimension(:) :: A
    integer(8) :: i, ans, b, c, d, c1, c2, j

    read(5,*) N
    allocate(A(N))
    read(5,*) (A(i), i = 1, N)

    

    c = 0
    d = 0
    c1 = 0
    c2 = 0

    do i = 1, N
        c = c + A(i)
        d = d + A(i) * A(i)
        if (c > 1000000007) then
            c1 = c / 1000000007
            c = c - c1 * 1000000007
        end if        
        if (d > 1000000007) then
            c2 = d / 1000000007
            d = d - c2 * 1000000007
        end if
 
    end do

    b = c**2-d

    if (mod(b,2) == 0) then
        ans = b / 2
        write(*,*) b
    else
        ans = (b+1000000007) / 2
    end if

    ans = mod(ans,1000000007)

    


    write(6,*) ans

    
end program C177