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 PyPy3 (7.3.0) (judge verdict: Accepted)

MOD = 10 ** 9 + 7

N = int(input())
A = list(map(int, input().split()))

rui = [A[0]] * N
for i in range(1, N):
	rui[i] = (rui[i - 1] + A[i]) % MOD
ans = 0
for i in range(1, N):
	ans = (ans + A[i] * rui[i - 1]) % MOD
print(ans)