import numpy as np

board=[[0]*4 for r in range(3)]

steamboat=[[0,0,0],[1,1,1],[0,1,0]]

def rotate(obj,axis,multiple):

	"""[ # z

		[[1,2,3], # y,x

		[4,5,6]],

		[[7,8,9],

		[10,11,12]]

	]"""

	matrices=[

		np.array([[1,0,0],[0,0,-1],[0,1,0]]),

		np.array([[0,0,1],[0,1,0],[-1,0,0]]),

		np.array([[0,-1,0],[1,0,0],[0,0,1]])

	]

	m=1

	for i in range(multiple): m=np.dot(m,matrices[axis])

	shape=np.array(obj.shape)

	shape_=abs(np.dot(shape,m))

	middle=(shape-1)/2

	middle_=(shape_-1)/2

	res=np.zeros(shape_)

	for (z,plane) in enumerate(obj):

		for (y,row) in enumerate(plane):

			for (x,item) in enumerate(row):

				point=np.array([z,y,x])

				point_=np.dot(point-middle,m)+middle_

				res[tuple(map(int,point_))]=item

	return res

def fits(board,piece,offset):

	(dz,dy,dx)=offset

	res=[]

	for (z,plane) in enumerate(piece):

		for (y,row) in enumerate(plane):

			for (x,item) in enumerate(row):

				if item==0: continue

				coords=(z+dz,y+dy,x+dx)

				if board[coords]: return None

				res.append(coords)

	return res

if __name__=="__main__":

	# for r in range(-2,3):

	# 	for c in range(-2,4):

	# 		x=fits(board,steamboat,(r,c))

	# 		if x: print((r,c),x)

	# print(rotZ([[0,1,0,0],[0,1,0,0],[0,1,0,0],[0,0,0,0]]))

	arr=np.array([ # z

		[[1,2,3], # y,x

		[4,5,6]],

		[[7,8,9],

		[10,11,12]]

	])

	print(rotate(arr,2,4))