Graph on a Plane

Limits: 4 sec., 512 MiB

You are given $n$ unique points $(x_i, y_i)$ on a two-dimensional plane.

A weighted undirected graph $G$ with real-valued weights is good if it satisfies the following conditions.

• $G$ contains $n$ vertices numbered $1$ through $n$.

• For each pair of vertices $(i, j)$, the shortest-path weight between vertices $i$ and $j$ in $G$ equals the Euclidean distance between points $(x_i, y_i)$ and $(x_j, y_j)$.

Find the minimum number of edges in a good graph.

Input

The first line contains an integer $n$ – the number of points.

The following $n$ lines contain two integers $x_i$ and $y_i$ – coordinates of the points.

Output

In a single line, print an integer – the minimum number of edges in a good graph.

Constraints

$1 \le n \le 2000$,

$|x_i|, |y_i| \le 10^9$.

All points are distinct.

Samples

Input (stdin) сopy	Output (stdout) сopy
4 0 0 4 3 4 2 0 4	6

Input (stdin) сopy	Output (stdout) сopy
5 0 0 1 0 0 2 -3 0 0 -4	8

Notes