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 Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(format t "~A~%"
        (loop with a = (loop repeat (read) collect (read))
              with result = 0
              for i2 on a
              for i = (first i2)
              while (cdr i2)
              do (incf result (* i (loop with result = 0
                                         for j in (rest i2)
                                         do (incf result j)
                                            (when (>= result 1000000007)
                                              (decf result 1000000007))
                                         finally (return result))))
              do (when (>= result 1000000007)
                   (setf result (mod result 1000000007)))
              finally (return result)))