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).

Examples

Input

3
1 2 3


Output

11


Input

4
141421356 17320508 22360679 244949


Output

437235829
#include <iostream>

using std::cin;
using std::cout;

int n, i;
long long v, s, a;
const long long m = 1e9 + 7;

int main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (i = 0; i != n; ++i) {
    cin >> v;
    a = (a + v * s) % m;
    s = (s + v) % m;
  }
  cout << a;
  return 0;
}
