Given $n$ points $(x_i, y_i)$ on the plane, define
$$d(i,j)=\sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}$$
Compute
$$\sum_{1 \le i < j \le n} d(i,j)$$
Input Format
The first line of the input contains an integer $n$.
The next $n$ lines each contain two integers $(x_i, y_i)$.
Output Format
Output a single real number — the answer. The absolute error must not exceed $10^{-4}$.
Sample Data
Sample Input
3
1 2
-1 3
0 -1Sample Output
9.5214512632858295782294770691381Sample Explanation
The answer is $d(1,2) + d(1,3) + d(2,3) = \sqrt{5} + \sqrt{10} + \sqrt{17}$.
Subtasks
For all test cases: $1 \le n \le 5 \times 10^5$, $-10^6 \le x_i, y_i \le 10^6$.
- Subtask 1 (10 points): $n \le 3\,000 $
- Subtask 2 (20 points): $n \le 40\,000 $
- Subtask 3 (30 points): $n \le 10^5 $
- Subtask 4 (20 points): $n \le 3 \times 10^5 $
- Subtask 5 (20 points): No additional constraints.