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)

mod = 1_000_000_007

n = gets.to_i
a = gets.split.map &:to_i

tmp0 = a.sum
tmp0 = ((tmp0 % mod) ** 2) % mod

tmp1 = a.sum { |e|
  e ** 2
}

tmp1 %= mod

puts tmp0 < tmp1 ? (tmp0 - tmp1 + mod) / 2 : (tmp0 - tmp1) / 2