# http://c...content-available-to-author-only...e.com/questions/49700/books-on-a-shelf
# http://r...content-available-to-author-only...l.it/mt7/4
 
from operator import*
from itertools import*
def f(t):
    m=1
    for l in(sorted(t,key=itemgetter(*o))for o in permutations(range(3))):
        c=1
        for k in range(len(l)-1):c+=all(i<=j for i,j in zip(l[k],l[k+1]))
        m=max(m,c)
    print m
 
f([(1, 1, 1)]) #1
f([(5, 2, 5), (1, 3, 5)]) #1
f([(5, 2, 5), (1, 2, 5)]) #2
f([(2, 2, 2), (2, 2, 2), (2, 2, 2), (1, 3, 6)]) #3
f([(1, 2, 5), (1, 3, 5), (1, 2, 8), (1, 2, 5), (7, 7, 7)]) #4
 
# WRONG!
 
#4 but should be 3
f([(5, 19, 3), (9, 4, 16), (15, 16, 13), (7, 4, 16), (1, 13, 14), (20, 1, 15), (9, 8, 19), (4, 11, 1)])
#6 but should be 5
f([(1, 1, 18), (1, 13, 7), (14, 1, 17), (8, 15, 16), (18, 8, 12), (8, 8, 15), (10, 1, 14), (18, 4, 6), (10, 4, 11), (17, 14, 17), (7, 10, 10), (19, 16, 17), (13, 19, 2), (16, 8, 13), (14, 6, 12), (18, 12, 3)])

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