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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

input = readlines()
n = input.shift.chomp.to_i
list = input.shift.chomp.split("\s").map{|x| x.to_i}

res = 0
list.each_with_index do |l1, i1|
  list.each_with_index do |l2, i2|
    next if i1 >= i2
    res += l1 * l2

    if res > 1000000007
      res = res % 1000000007
    end

  end
end

puts res