Chinna and Chinnu are very fond of games and love to dominate one another. But most of the times, they fight with each other and hence to keep them busy Rocky takes an initiative and present them two gifts. A Big co-ordinate board with integral co-ordinates and A toy train station with variable number of platforms to Chinna and Chinnu respectively.

As a part of the game, Rocky gives Chinna 'N' co-ordinates (x >= 0 && y >= 0) and asks him to find a minimal subset of these points such that every point lies in/on the rectangle (0 <= x <= 23 && 0 <= y <= 59) and the points has to cover the maximum area possible in that rectangle (i.e, every point in that rectangle has to be in\on the polygon formed by the points in the subset).

He takes this subset to Chinnu and tells her that this is a set of time of arrivals of trains which comes to her toy train station. The halt of each train at the station depends on the time i.e., hours * 60 + minutes , if the time is a prime then the halt is 5 minutes, if it's a odd composite then halt is 3 minutes else if it's a even composite then the halt is 2 minutes. He asks her to build a station with minimum number of platforms sufficient to accompy all the trains.

Your job is to help Rocky check them to play fair. For each set Rocky wants to give to Chinna. You need find the correct output and give it to Rocky.

Input :

First line , Number of coordinates N
Next N lines, two space separated integers X and Y co-ordinates

Constraints:

    1 <= N <= 10^5
0 <= X,Y <= 10^9

Output :

First line, number of points in the subset M
Next M lines contain two space separated integers x,y co-ordinates of the points respectively
Next line, a single integer containing number of platforms Chinnu needs to build