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 sum_of_product_of_pairs
  implicit none
  integer(8), parameter :: m = 1000000007
  integer :: n, i
  integer(8) :: a(200000) = 0, s = 0, x = 0
  read(*,*) n
  read(*,*) a(1:n)
  s = a(n)
  do i = n - 1, 1, -1
    x = mod(x + s * a(i), m)
    s = s + a(i)
    if (s >= m) s = s - m
  end do
  write(*,'(i0)') x
end program sum_of_product_of_pairs