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: Accepted)

program ABC177C
    implicit none
    integer(8)::N,m=1000000007,i,ans=0
    integer(8),allocatable::A(:),S(:)
    read*,N
    allocate(A(N))
    allocate(S(N))
    read*,A
    do i=1,N
        if(i==1)then
            S(i)=mod(A(i),m)
        else
            S(i)=mod(S(i-1)+A(i),m)
        end if
    end do

    do i=1,N-1
        if(S(N)-S(i)<0)then
            ans=ans+mod(A(i)*(m+S(N)-S(i)),m)
        else
            ans=ans+mod(A(i)*(S(N)-S(i)),m)
        end if
        ans=mod(ans,m)
    end do
    print'(i0)',mod(ans,m)
end program ABC177C