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 Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

combinations :: Int -> [a] -> [[a]]
combinations n xs = comb n (length xs) xs where
  comb 0 _ _ = [[]]
  comb r n a@(x:xs)
    | n == r    = [a]
    | otherwise = map (x:) (comb (r - 1) (n - 1) xs) ++ comb r (n - 1) xs

main = do
 getLine
 aList <- map read . words <$> getLine :: IO [Integer]
 let a = combinations 2 aList
 let c = map (flip mod 1000000007) $ map product a
 let b = (foldl (+) 0 c) `mod` 1000000007
 print b