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: Wrong Answer)

N = gets.to_i
A = gets.chomp.split.map(&:to_i)
sum = 0
x = 0

(0..N-1).each do |i|
  sum += A[i]**2%1000000007
  sum %= 1000000007
  x += A[i]
  x %= 1000000007
end

y = x**2%1000000007

if y>=sum
  puts (y-sum)/2
else
  puts (y+1000000007-sum)/2
end