Find the Worlds

There are M known worlds in a two-dimensional universe. Each world contains one or more cities, and each city will be located in one of those M worlds. A city is a point in the 2D universe that is represented by an integer coordinate (x,y). No more than 1 city will share the same coordinate.

The distance between two cities is the euclidean distance (the distance of the straight line) between the two points. All the cities in the universe are laid out satisfying the following conditions:

• Distance between any two cities of any given world ≤ 10,000
• Distance between any two cities from different worlds > 10,000

Given the location of cities, find the number of worlds in the universe and the number of cities in each world.

Input Format

The first line contains the number of cities, N
Each of the next N lines contains 2 integers separated by a space representing X,Y coordinate of a city.

Output Format

The first line should contain the number of worlds in the universe, M
The second line should contain the number of cities in each of those M worlds. These M integers should be separated by a space and sorted in the ascending order.

Constraints

• 1 \(\leq\) N \(\leq\) 10⁷
• -10⁹ \(\leq\) X, Y \(\leq\) 10⁹ where (X,Y) are the integer coordinates of cities.

At least 30% of test cases will have N \(\leq\) 10,000

Limits

• Time Limit: 2s
• Memory Limit: 256MB

Sample Input 0

5
2 1
3 1
2 100000
2 100002
1 1

Sample Output 0

2
2 3