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 C177
    implicit none
    integer(8) :: N
    integer(8), allocatable, dimension(:) :: A
    integer(8) :: i, j, ans

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

    ans = 0
    do i = 1, N-1
        do j = i+1, N
            ans = ans + A(i)*A(j)

            if (ans > 1000000007) then
                ans = mod(ans,1000000007)
            end if
        end do
    end do

    write(6,*) ans


    
end program C177