Integer

INPUT FILE: integer.in
OUTPUT FILE: integer.out

Consider the following function of a positive integer:

f(n) = (1¹ + 2² + 3³ + ... + nⁿ)/n

You must determine, for a given n, whether f(n) is an integer or not. The value of n will be between 1 and 40000.
Your program should run each test case in no more than 2 seconds.

INPUT

You will be given a series of integers, one to a line, terminated by the number 0.

OUTPUT
For each integer write out "f(n) is an integer" or "f(n) is not an integer" accordingly.

Sample Input File

1
3
4
0

Output for Sample Input

f(1) is an integer
f(3) is not an integer
f(4) is an integer