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 Julia (1.4.0) (judge verdict: Accepted)

parse_input(type=String, x=readline()) = begin
  type == String && return x
  parse(type, x)
end
parse_inputs(type=String) = parse_input.(type, split(readline()))

function solve()
  _ = parse_input()
  A = parse_inputs(BigInt)
  end_a = A[end]
  ans = 0
  for a in A[end-1:-1:1]
    ans += a*end_a
    end_a += a
  end
  mod(ans, (10^9)+7)
end

println(solve())