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: Time Limit Exceeded)

parseInt(x) = parse(Int128, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)
using Primes
function main()
  N = parseInt(readline())
  A = parseMap(split(readline()))

  #i=BigInt(1)
  # println(factor(K)) ; println(collect(factor(K)))
  # println(isprime(K))
  # for item in collect(factor(K))
  #   println("$(item.first): $(item.second)")
  # end
  # println(in(79=>1 ,collect(factor(K))))

  #exit()
  seki = Int128(0)
  for i in 1:N-1
    for j in i+1:N
      seki += mod(Int128(A[i]*A[j]),Int128(10^9)+7)
      #println(i,":",j,":",seki,":",A[i]*A[j])
    end
  end
  println(mod(seki,Int128(10^9)+7))

end
main()