# arrange the numbers from 1 to 2n in pairs
# so that the sum of each pair is a square
# for what numbers is this possible?

def GetPossibles(max):
	for n in range(1,max):
		
		# make a list of the needed squares
		def getSquares(n):
			squares = []
			i=2
			while i**2<4*n:
				squares.insert(0,i**2)
				i = i+1
			# print squares
			return squares

		# this makes a list of lists:
		# what you can add to each number to get a square
		# the first element, being element 0, will be ignored
		# after that, each list corresponds to its index
		def getOptions(n):
			theOptions = [None]
			squares = getSquares(n)
			for number in range (1,2*n+1):
				complements=[]
				for square in squares:
					if (square > number) and (square != 2 * number) and (square - number < 2*n+1):
						complements.append(square - number)
				theOptions.append(complements)
			# print theOptions
			return theOptions

		# pairs is the list we are building for n
		# available is a list of the unused numbers
		def getPairs(n,pairs,available):
			if len(pairs) == n:
				return pairs
			number = available[0]
			for partner in theOptions[number]:
				if partner in available:
					newPair = (number,partner)
					result = getPairs(n,pairs + [newPair],[x for x in available if x not in newPair])
					if result is not None:
						return result
			return None

		theOptions = getOptions(n)
		theOutput = getPairs(n,[],range(2*n,0,-1))
		if theOutput != None:
			print n

GetPossibles(44)