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 q_3
  implicit none
  integer(8) :: n,i,j,mo,seki,sum,tmp
  integer(8),allocatable :: A(:)

  mo = 10**9+7
  read(*,*) n
  allocate(A(n))
  read(*,*) A
  seki = 0
  sum = 0
  do i =1,n
     sum = sum + A(i)
  end do
!  write(*,*)sum                                                                                                                                                                                                  
  tmp = sum
  do i =1,n-1
     tmp = tmp - A(i)
 !    write(*,*)tmp                                                                                                                                                                                               
     seki = seki + mod(A(i)*mod(tmp,mo),mo)
!     do j = i+1,n                                                                                                                                                                                                
!        seki = seki + mod(A(i)*A(j),mo)                                                                                                                                                                          
!     end do                                                                                                                                                                                                      
  enddo
!  write(*,*) seki                                                                                                                                                                                                
  write(*,*) mod(seki,mo)

end program q_3