#!/usr/bin/env python

#  Problem 5:
#
#  2520 is the smallest number that can 
#  be divided by each of the numbers 
#  from 1 to 10 without any remainder.
# 
#  What is the smallest positive number 
#  that is evenly divisible by all of the 
#  numbers from 1 to 20?
#

import decorators			# Typically imported to compute execution duration of functions.
import time					# Typically imported for sleep function, to slow down execution in terminal.
import typing

def evenly_divisible(candidate: int,factors: list):
	"""
	Determines if the supplied integer candidate is 
	evenly divisble by the supplied list of factors.
	
		evenly_divisible(candidate: int, factors: list)

			param 'candidate': Integer to be tested.
			param 'factors': List of factors for the modulus operator.
			
	"""
	
	modulus_sum = 0

	for n in factors:
		modulus_sum += candidate%n
	
	if modulus_sum == 0: 
		return True
	else:
		return False


@decorators.function_timer
def main():

	# Receive problem inputs...
	smallest_factor = 1
	largest_factor = 17

	# Compute intermediate inputs
	factor_list = [int(i) for i in range(smallest_factor,largest_factor+1)]
	maximum_solution_bound = 1
	for f in factor_list:
		maximum_solution_bound *= f
	
	# Initialize loop parameters
	n = 10
	test_passed = False

	while n<maximum_solution_bound and not test_passed:
		test_passed = evenly_divisible(n,factor_list)
		if not test_passed:
			n += 1



	print("The largest palindrome number which is a product of two numbers of length {} is {} ... ".format(factor_list,n))

main()