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import fileinput
import re
from copy import deepcopy
from collections import defaultdict
import math
R = 10
C = 10
def rotate(T):
TR = len(T)
TC = len(T[0])
# takes (r,c) to (c, R-1-r)
RET = [["?" for _ in range(TR)] for _ in range(TC)]
for r in range(TR):
for c in range(TC):
RET[c][TR - 1 - r] = T[r][c]
return RET
def flip(T):
return list(reversed(T))
def flip2(T):
return [list(reversed(row)) for row in T]
def poss(T):
ans = set()
flips = [deepcopy(T), flip(T)] # , flip2(T), flip(flip2(T))]
for _ in range(4):
for i in range(len(flips)):
ans.add(tuple([tuple(row) for row in flips[i]]))
flips[i] = rotate(flips[i])
return ans
L = list([l.strip() for l in fileinput.input()])
L.append("")
G = {}
name = None
piece = []
for l in L:
if "Tile" in l:
name = int(l.split()[1][:-1])
elif l:
piece.append(list(l))
else:
G[name] = piece
piece = []
# for k,T in G.items():
# print(k)
# for row in T:
# print(''.join(row))
EDGE = {}
for k, T in G.items():
left = []
right = []
top = []
bottom = []
for r in range(R):
left.append(T[r][0])
right.append(T[r][R - 1])
for c in range(C):
top.append(T[0][c])
bottom.append(T[R - 1][c])
edges = [tuple(x) for x in [left, right, top, bottom]]
EDGE[k] = set([x for x in edges] + [tuple(reversed(x)) for x in edges])
E = defaultdict(set)
# Assumes if two pieces have identical boundaries they will actually be adjacent in the final puzzle
start = None
ans = 1
for k1, ET in EDGE.items():
nbrs = 0
for k2, EU in EDGE.items():
if k1 != k2:
if ET & EU:
E[k1].add(k2)
if len(E[k1]) == 2:
start = k1
ans *= k1
print(ans)
GR = int(math.sqrt(len(EDGE)))
GC = int(math.sqrt(len(EDGE)))
USED = set()
assert len(EDGE) == GR * GC
PLACE = [[None for _ in range(GR)] for _ in range(GC)]
PLACE[0][0] = start
PLACE[0][1], PLACE[1][0] = E[start]
USED.add(PLACE[0][0])
USED.add(PLACE[0][1])
USED.add(PLACE[1][1])
D = [(-1, 0), (0, 1), (1, 0), (0, -1)]
#####
####
###
##
#
while True:
if len(USED) == GR * GC:
break
for r in range(GR):
for c in range(GC):
if PLACE[r][c] is not None:
continue
opts = set([k for k in E.keys() if k not in USED])
for dr, dc in D:
rr, cc = r + dr, c + dc
if 0 <= rr < GR and 0 <= cc < GC and PLACE[rr][cc]:
opts = opts & E[PLACE[rr][cc]]
if len(opts) == 1:
chosen = list(opts)[0]
PLACE[r][c] = chosen
assert chosen not in USED
USED.add(chosen)
# Does the boundary of p1 match p2, assuming p2 is in the direction (dr,dc)?
def matches(p1, p2, dr, dc):
if dr == -1: # up, so top of p1 should match bottom of p2
for c in range(C):
if p1[0][c] != p2[R - 1][c]:
return False
return True
elif dc == 1: # right, so right of p1 should match left of p2
for r in range(R):
if p1[r][C - 1] != p2[r][0]:
return False
return True
elif dr == 1:
for c in range(C):
if p1[R - 1][c] != p2[0][c]:
return False
return True
elif dc == -1:
for r in range(R):
if p1[r][0] != p2[r][C - 1]:
return False
return True
else:
assert False
PIECES = [[None for _ in range(GR)] for _ in range(GC)]
for r in range(GR):
for c in range(GC):
opts = poss(G[PLACE[r][c]])
for dr, dc in D:
rr, cc = r + dr, c + dc
if 0 <= rr < GR and 0 <= cc < GC:
ok_nbr = set()
opts_nbr = poss(G[PLACE[rr][cc]])
for o1 in opts:
for o2 in opts_nbr:
if matches(o1, o2, dr, dc):
ok_nbr.add(o1)
opts = opts & ok_nbr
# Assumes that every piece has only one orientation that can match its neighbors
assert len(opts) == 1
PIECES[r][c] = list(opts)[0]
for r in range(GR):
for c in range(GC):
for dr, dc in D:
rr, cc = r + dr, c + dc
if 0 <= rr < GR and 0 <= cc < GC:
p1 = PIECES[r][c]
p2 = PIECES[rr][cc]
assert matches(p1, p2, dr, dc)
IMAGE = [["?" for _ in range(GC * (C - 2))] for _ in range(GR * (R - 2))]
for r in range(GR):
for c in range(GC):
T = PIECES[r][c]
assert T in poss(G[PLACE[r][c]])
for rr in range(1, len(T) - 1):
for cc in range(1, len(T[rr]) - 1):
IMAGE[r * (R - 2) + (rr - 1)][c * (C - 2) + (cc - 1)] = T[rr][cc]
M = [" # ", "# ## ## ###", " # # # # # # "]
MR = len(M)
MC = len(M[0])
for row in M:
assert len(row) == MC
IR = len(IMAGE)
IC = len(IMAGE[0])
assert len(IMAGE) == IR
for row in IMAGE:
assert len(row) == IC
for IM in poss(IMAGE):
assert len(IM) == IR
assert len(IM[0]) == IC
IS_M = [[False for _ in range(len(IM[0]))] for _ in range(len(IM))]
has_monster = False
for r in range(IR):
for c in range(IC):
is_monster = True
for mr in range(MR):
for mc in range(MC):
if not (0 <= r + mr < IR and 0 <= c + mc < IC):
is_monster = False
else:
if M[mr][mc] == "#" and IM[r + mr][c + mc] != "#":
is_monster = False
if is_monster:
has_monster = True
for mr in range(MR):
for mc in range(MC):
if M[mr][mc] == "#":
IS_M[r + mr][c + mc] = True
# Assumes only one orientation has sea monsters
if has_monster:
ans = 0
for r in range(IR):
for c in range(IC):
if IM[r][c] == "#" and not IS_M[r][c]:
ans += 1
print(ans)
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