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)

n = gets.chomp.to_i
arr = gets.chomp.split(' ').map(&:to_i)
mod = 1000000007

i = 0
sum = 0
each_sum = 0
while i < n-1
  each_sum += arr[i]
  sum += arr[i] * (arr.sum - each_sum)
  # a*b+ a*c + a*d + b*c + b*d + c*d  
  # a(b+c+d) + b(c+d) + 
  # 
  #
  i += 1
end
puts sum%mod