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 Julia (1.4.0) (judge verdict: Accepted)

function main()
    N = parse(Int, readline())
    A = []
    for i ∈ 1:N
        a = parse(Int,  readuntil(stdin, " "))
        append!(A, [a])
    end

    sum = 0
    accumulated = 0
    for i ∈ 2:N
        accumulated = mod(accumulated + A[i-1], 7+10^9)
        sum = mod(sum + accumulated * A[i], 7+10^9)
    end

    println(mod(sum, 7+10^9))
end

main()