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from sys import argv
from math import log, sqrt, floor
# check if n is within EPS of being a whole number
def is_whole(n):
EPS = 1e-10
round = int(f'{n:.0f}')
return abs(round - n) < EPS
# My algorithm is this:
# Loop over all the m's from 2 to sqrt(N)
# If m can be raised to an integer power to equal N, then log_m N is an integer
N = int(argv[1])
logn = log(N)
found = False
for m in range(2, int(sqrt(N))+1):
n = logn / log(m)
if is_whole(n):
print(f'{m}^{n:.0f}')
found = True
if not found:
print(0)
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