In one country, there are N cities. All of them are located on a plane with Cartesian coordinates. The government of this country decided to build roads between these cities. However, they have several requirements:

To earn more points in the trust fund of the country’s residents, the government wants to build as many roads as possible while adhering to these requirements. Help them find this number.

The first line contains an integer N — the number of cities in the country (2 ≤ N ≤ 10⁵).

Each of the following N lines contains two integers x_i, y_i separated by a space — the coordinates of the i-th city (−10⁹ ≤ x_i, y_i ≤ 10⁹).

It is guaranteed that no two cities have the same coordinates.

Output the maximum number of roads that can be built while satisfying the requirements.