#  Problem 3:
#
#  A palindromic number reads the same both ways. 
#  The largest palindrome made from the product 
#  of two 2-digit numbers is 9009 = 91 × 99.
#  
#  Find the largest palindrome made from the 
#  product of two 3-digit numbers.
#

import decorators
import time

# Create function that finds the next
# prime number when supplied with an
# intitial integer.

def is_palindrome(candidate):
	"""
	Returns a boolean to confirm if the passed
	integer is a palindrome.
	
		is_palindrome(candidate)

			param 'candidate': Integer to test for palindrom-iness.
			
	"""

	# Convert maximum candidate to a list ...
	listed_candidate = [int(i) for i in str(candidate)]
	flipped_candidate = [int(i) for i in str(candidate)]
	#print("{}".format(listed_candidate))

	# Determine length of maximum candidate, and manipulate.	
	num_digits = listed_candidate.__len__()
	digit_flips = int(num_digits/2)

	for i in range(1,digit_flips):
		#print("{}".format(i))
		flipped_candidate[-i-1] = flipped_candidate[i]
	flipped_candidate[-1] = flipped_candidate[0]

	#print("{}".format(flipped_candidate))

	# Compare ...		
	if listed_candidate == flipped_candidate:
		return True
	else:
		return False

@decorators.function_timer
def main():

	# Define the problem inputs... 
	factor_length = 3
	
	# Calculate intermediate inputs...
	max_factor = 10**(factor_length)-1
	product_of_factors = max_factor * max_factor # Maximum candidate for palindrome test. 
	
	# Initialize loop parameters...
	n = max_factor
	m = max_factor
	n_has_token = False
	test_passed = False
	palindrome_list=[]

	while (n*m)>0:
	
		# Test for "palindrom-iness" ...
		print("{} * {} = {}".format(n,m,n*m))
		test_passed = is_palindrome(n*m)
#		if not test_passed and n_has_token:	
#			n -= 1
#			if n == 1:
#				n_has_token = False
#				n = max_factor
#		elif not test_passed and not n_has_token:
#			m -= 1
#			n_has_token = True
#		else:
#			palindrome_list.append(n*m)
#
		if test_passed:
			palindrome_list.append(n*m)
			if n_has_token:
				n -= 1
				if n ==1:
					n_has_token = False
					n = max_factor
			if not n_has_token:
				m -= 1
				n_has_token = True
		
		if not test_passed:
			if n_has_token:
				n -= 1
				if n ==1:
					n_has_token = False
					n = max_factor
			if not n_has_token:
				m -= 1
				n_has_token = True


			

		
	print("{}".format(max(palindrome_list)))
#	print("{} * {} = {}".format(n,m,n*m))

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



main()