5D Chests
Statement
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.
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.
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
2 ≤ C ≤ 10,000
Example
Input
5 8
Output
1141 236 216
Tags
Flood fill
Difficulty
Medium
Test cases
N=5 Test
Input
5
8
Output
1141
236
216
N=5 Validator
Input
5
23
Output
1382
74
651
N=10 Test
Input
10
77
Output
29552
3064
9090
N=10 Validator
Input
10
7777
Output
32251
3562
23325
N=15 Test
Input
15
11
Output
268939
1611
49408
N=15 Validator
Input
15
1111
Output
145380
38105
22030
N=20 Test
Input
20
9
Output
653072
143339
271
N=20 Validator
Input
20
99
Output
891383
137353
182225
Solution language
Solution
Stub generator input