import euler
n = 61
pent_nums = []
cache = {}
while True:
if euler.p(n, pent_nums, cache) % 1000000 == 0:
break
n += 1
print n
= 2 + 2 + 1 + 1
= 2 + 1 + 1 + 1 + 1
= 1 + 1 + 1 + 1 + 1 + 1
7 = 7
= 6 + 1
= 5 + 2
= 5 + 1 + 1
= 4 + 3
= 4 + 2 + 1
= 4 + 1 + 1 + 1
= 3 + 3 + 1
= 3 + 2 + 2
= 3 + 2 + 1 + 1
= 3 + 1 + 1 + 1 + 1
= 2 + 2 + 2 + 1
= 2 + 2 + 1 + 1 + 1
= 2 + 1 + 1 + 1 + 1 + 1
= 1 + 1 + 1 + 1 + 1 + 1 + 1
'''
from euler import partition as p
assert 7 == p(5)
assert 56 == p(11)
assert 190569291 == p(100)-1 # excluding itself (1-partition)
print p(100)-1
= 3 + 1 + 1 + 1
= 2 + 2 + 2
= 2 + 2 + 1 + 1
= 2 + 1 + 1 + 1 + 1
= 1 + 1 + 1 + 1 + 1 + 1
7 = 7
= 6 + 1
= 5 + 2
= 5 + 1 + 1
= 4 + 3
= 4 + 2 + 1
= 4 + 1 + 1 + 1
= 3 + 3 + 1
= 3 + 2 + 2
= 3 + 2 + 1 + 1
= 3 + 1 + 1 + 1 + 1
= 2 + 2 + 2 + 1
= 2 + 2 + 1 + 1 + 1
= 2 + 1 + 1 + 1 + 1 + 1
= 1 + 1 + 1 + 1 + 1 + 1 + 1
'''
from euler import partition as p
assert 7 == p(5)
assert 56 == p(11)
assert 190569291 == p(100) - 1 # excluding itself (1-partition)
print p(100) - 1
'''
This problem is a variant of P0076
'''
from euler import partition as p
n = 0
while True:
n += 1
pn = p(n)
if pn%1000000==0:
break
print n, pn
