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import sys
triangle = set([ n*(n+1)/2 for n in range(45,141) ])
square = set([ n*n for n in range(32,99) ])
pentagonal = set([ n*(3*n-1)/2 for n in range(26,82) ])
hexagonal = set([ n*(2*n-1) for n in range(23,71) ])
heptagonal = set([ n*(5*n-3)/2 for n in range(21,64) ])
octagonal = set([ n*(3*n-2) for n in range(19,59) ])
whole = set(triangle | square | pentagonal | hexagonal | heptagonal | octagonal)
def check_cond(testset):
check = 0
for e in testset:
if e in octagonal:
check |= 1
elif e in heptagonal:
check |= 2
elif e in hexagonal:
check |= 4
elif e in pentagonal:
check |= 8
elif e in square:
check |= 16
elif e in triangle:
check |= 32
return check == 63
for i0 in whole:
t0 = i0 % 100
tail0 = [ n for n in whole if t0*100 < n < (t0+1)*100 ]
for i1 in tail0:
t1 = i1 % 100
tail1 = [ n for n in whole if t1*100 < n < (t1+1)*100 ]
for i2 in tail1:
t2 = i2 % 100
tail2 = [ n for n in whole if t2*100 < n < (t2+1)*100 ]
for i3 in tail2:
t3 = i3 % 100
tail3 = [ n for n in whole if t3*100 < n < (t3+1)*100 ]
for i4 in tail3:
t4 = i4 % 100
tail4 = [ n for n in whole if t4*100 < n < (t4+1)*100 ]
for i5 in tail4:
if i5 % 100 != i0 / 100:
continue
s = set([i0, i1, i2, i3, i4, i5])
if len(s) == 6 and check_cond(s):
print sum(s)
sys.exit(0)
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