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 OCaml (4.10.0) (judge verdict: Time Limit Exceeded)

let as_num_list s =
  let splitted = String.split_on_char ' ' s in
  List.map int_of_string splitted

let main () =
  let n = Scanf.sscanf (read_line ()) "%d" (fun x -> x) in
  let as_str = read_line () in
  let a_list = as_num_list as_str in
  let sum = ref 0 in
  (
    for i = 0 to n - 2 do
      for j = i + 1 to n - 1 do
        sum := (!sum +
                  (List.nth a_list i) * (List.nth a_list j)) mod 1000000007
      done
    done;
    Printf.printf "%d" !sum;
    print_newline ()
  )

let _ = main ()