# 
# Solution to Project Euler problem 44
# Copyright (c) Project Nayuki. All rights reserved.
# 
# https://www.nayuki.io/page/project-euler-solutions
# https://github.com/nayuki/Project-Euler-solutions
# 

import itertools, sys
if sys.version_info.major == 2:
	range = xrange


def compute():
	pentanum = PentagonalNumberHelper()
	min_d = None  # None means not found yet, positive number means found a candidate
	# For each upper pentagonal number index, going upward
	for i in itertools.count(2):
		pent_i = pentanum.term(i)
		# If the next number down is at least as big as a found difference, then conclude searching
		if min_d is not None and pent_i - pentanum.term(i - 1) >= min_d:
			break
		
		# For each lower pentagonal number index, going downward
		for j in range(i - 1, 0, -1):
			pent_j = pentanum.term(j)
			diff = pent_i - pent_j
			# If the difference is at least as big as a found difference, then stop testing lower pentagonal numbers
			if min_d is not None and diff >= min_d:
				break
			elif pentanum.is_term(pent_i + pent_j) and pentanum.is_term(diff):
				min_d = diff  # Found a smaller difference
	return str(min_d)


# Provides memoization for generating and testing pentagonal numbers.
class PentagonalNumberHelper(object):
	def __init__(self):
		self.term_list = [0]
		self.term_set = set()
	
	def term(self, x):
		assert x > 0
		while len(self.term_list) <= x:
			n = len(self.term_list)
			term = (n * (n * 3 - 1)) >> 1
			self.term_list.append(term)
			self.term_set.add(term)
		return self.term_list[x]
	
	def is_term(self, y):
		assert y > 0
		while self.term_list[-1] < y:
			n = len(self.term_list)
			term = (n * (n * 3 - 1)) >> 1
			self.term_list.append(term)
			self.term_set.add(term)
		return y in self.term_set


if __name__ == "__main__":
	print(compute())