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)

import qualified Data.ByteString.Char8 as B
import Data.Maybe

value = 10^9+7

main = do
    n <- fst . fromJust . B.readInt <$> B.getLine
    aa <- map (fst . fromJust . B.readInt) . B.words <$> B.getLine
    print $ flip mod value . sum $ map (answer aa) [(i,j) | i <- [0..n-1], j <- [0..n-1],  i < j]

answer aa (i,j) = (aa!!i * aa!!j) `mod` value