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Checking cube
Given a integer N. Find number of possible ways to represent N as a sum of at most five cubes.

Input

First line contains N.

1<=N<=125000.

Output

Output the result

Sample

Input

4

1
64

905

15436

 

Output
#1 1

#2 2

#3 0

#4 12

 

Giải thích:
+ Cách 1: 64 = 27 + 27 + 8 + 1 + 1
+ Cách 2: 64 = 64 + 0  + 0 + 0 + 0