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## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Goal

Pirx the Pilot is flying his spaceship through hyperspace in search of gold. Given a 5D realm with all dimensions ranging from 1 to N, each location (x,y,z,w,v) is either a chest of gold (1) or a barrier (0) as determined by the function:

f(x,y,z,w,v)=isprime(1+ mod(x*y*z*w*v,C))

The barriers form rooms in hyperspace (Pirx can only move along the five dimensions, no diagonals). Help Pirx search every room and find all the gold.
Input
First line: The size N of each dimension.
Second line: The constant C for terrain generation.
Output
First line: The total number of gold chests.
Second line: The number of rooms that contain at least one chest.
Third line: The largest number of gold chests in one room.
Constraints
3 ≤ N ≤ 20
2 ≤ C ≤ 10,000
Example
Input
```5
8```
Output
```1141
236
216```

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