#! /usr/local/python # Factorize numbers. # The algorithm is not efficient, but easy to understand. # If there are large factors, it will take forever to find them, # because we try all odd numbers between 3 and sqrt(n)... import sys from math import sqrt error = 'fact.error' # exception def fact(n): if n < 1: raise error # fact() argument should be >= 1 if n == 1: return [] # special case res = [] # Treat even factors special, so we can use i = i+2 later while n%2 == 0: res.append(2) n = n/2 # Try odd numbers up to sqrt(n) limit = sqrt(n+1) i = 3 while i <= limit: if n%i == 0: res.append(i) n = n/i limit = sqrt(n+1) else: i = i+2 res.append(n) return res def main(): if len(sys.argv) > 1: for arg in sys.argv[1:]: n = eval(arg) print n, fact(n) else: try: while 1: n = input() print n, fact(n) except EOFError: pass main()