Problems
Universal numbers
Universal numbers
Ibrahim loves to play with numbers. He recently learned how to raise numbers to a power, and he really likes it. Farhad knows this, so he asked Ibrahim the following question: in how many different ways can one represent n as the sum of three numbers with the same integer non-negative base k raised to a non-negative integer.
In other words, you must find the number of different fours of non-negative integers (k, a, b, c), satisfying the equality n = ka
+ kb
+ kc
(k > 0).
Help Ibrahim to solve this problem.
Input
One integer n (4 ≤ n ≤ 1018
).
Output
Print one integer - the amount of different fours of numbers.
Input example #1
4
Output example #1
3
Input example #2
5
Output example #2
6
Input example #3
10
Output example #3
9