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)

main = do
  n <- readLn
  xs <- map read . words <$> getLine :: IO [Integer]
  print $ solve n xs

solve n xs = foldl (\x y -> (x + y) `mod` (1000000000 + 7)) 0 $ do
  i <- [1..n-1]
  return $ xs !! (i-1) * ((ss !! n) - (ss !! i))
  where
    ss = scanl (+) 0 xs