Problem Statement

For $2$ points $P,Q$ on the $xy$ plane, we define $rect(P,Q)$ as follows.

\[rect(P,Q) := \begin{cases} \text{すべての辺が}\ x\ \text{軸または}\ y\ \text{軸と平行であり、}\ P\ \text{と}\ Q\ \text{を頂点として持つ長方形の面積} & (P\ \text{と}\ Q\ \text{の}\ x\ \text{座標と}\ y\ \text{座標がともに異なる場合}) \\ 0 & (\text{それ以外の場合}) \\ \end{cases} \] In the formula above, the value is the area of the rectangle whose sides are all parallel to the x-axis or the y-axis and which has P and Q as vertices if P and Q differ in both their x-coordinates and their y-coordinates, and 0 otherwise.

You are given an integer $N$ and $N$ points $P_1(X_1, Y_1), P_2(X_2, Y_2), \dots, P_N(X_N, Y_N)$ on the $xy$ plane. For a point $Q$, we define $f(Q)$ as follows.

\[ f(Q) := \displaystyle \sum_{i=1}^N rect(P_i, Q) \]

Find the minimum value of $f(Q)$ when the point $Q$ is chosen appropriately.

Input

$N$
$X_1$ $Y_1$
$X_2$ $Y_2$
$\vdots$
$X_N$ $Y_N$

• $1 \leq N \leq 10^5$
• $0 \leq X_i, Y_i \leq 10^6$ $(1 \leq i \leq N)$
• All input values are integers.

Output

Output the answer. It can be proved that the answer is an integer under the constraints of this problem. (Added at 21:58)

Sample

3
0 0
1 1
2 2

1

2
10 10
10 10

0

10
58 74
60 3
83 30
51 85
25 70
82 62
47 8
25 28
77 93
3 69

3876