x

problems.py

def factorial_sumofdigits(n):
    val = 1
    for i in xrange(1,n+1):
        val *= i
    return sum([int(c) for c in str(val)])

for i in xrange(1,10000):
    f = factorial_sumofdigits(i)
    print i, f
    if f == 8001:
        print 'DONE'
        break

# used the following js to get this:
# x = []
# $('p').each(function() { x.push($(this).parents().length); });
p_depths = [3, 9, 7, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 9, 9, 9, 6, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 7, 8, 8, 9, 9, 8, 8, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 7, 6, 5, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9, 9, 8, 8, 8, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 7, 6, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 7, 7, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 9, 9, 9, 9, 8, 8, 8, 8, 8, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 5, 6, 6, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 7, 7, 7, 7, 7, 7, 7, 5, 6, 6, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 7, 7, 7, 8, 8, 8, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 6, 8, 8, 8, 8, 8, 8, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 8, 8, 8, 8, 7, 7, 7, 8, 8, 8, 8, 8, 8, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 5, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 6, 6, 6, 7, 5, 6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 7, 5, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 6, 6, 6, 5, 5, 5, 6, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 8, 8, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 6, 8, 8, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 8, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 8, 8, 8, 8, 6, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 6, 6, 6, 6, 5, 6, 6, 5, 6, 6, 6, 6, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 6, 6, 5, 7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 7, 6, 8, 6, 7, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 6, 6, 7, 7, 7, 7, 6, 5, 5, 8, 8, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 6, 6, 6, 6, 7, 6, 5, 7, 7, 7, 7, 7, 7, 7, 7, 5, 6, 6, 6, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 6, 6, 6, 6, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 3, 3, 7, 7, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 5, 7, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 7, 7, 6, 6, 6, 7, 7, 7, 6, 6, 6, 3, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 3, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 5, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 7, 5, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 6, 6, 6, 5, 5, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 3, 3, 4, 6, 6, 6, 4, 4, 4, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 7, 7, 5, 6, 6, 5, 7, 7, 7, 7, 7, 6, 6, 6, 7, 7, 7, 7, 6, 6, 6, 5, 6, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 5, 5, 6, 6, 5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 4, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 3, 4, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 5, 5, 5, 4, 4, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 7, 7, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 5, 6, 6, 5, 5, 5, 5, 6, 5, 7, 7, 7, 7, 6, 6, 6, 6, 6, 3, 3, 5, 4, 4, 5, 5, 5, 4, 4, 4, 4, 4, 4, 5, 5, 4, 4, 4, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 3, 3, 5, 5, 5, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 5, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 5, 7, 7, 7, 6, 6, 6, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 6, 5, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 5, 5, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 7, 7, 6, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 5, 5, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 7, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 7, 7, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 8, 8, 8, 7, 7, 7, 7, 7, 7, 8, 8, 7, 9, 9, 9, 9, 8, 8, 8, 8, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 7, 7, 7, 7, 8, 8, 7, 7, 7, 6, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 6, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 6, 9, 9, 8, 8, 8, 8, 8, 7, 8, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 7, 7, 7, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 6, 9, 9, 9, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 9, 8, 8, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 7, 8, 9, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 7, 6, 6, 7, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 7, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 7, 7, 6, 7, 7, 7, 8, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 5, 4, 4, 5, 6, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 6, 6, 6, 6, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 5, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 5, 5, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 4, 3]
import numpy
print numpy.std(p_depths)

max_freq = 2520

total_words = sum([ float(max_freq)/float(i) for i in xrange(1,901)])
words = 0
for i in xrange(1,901):
    words += float(max_freq)/float(i)
    if words > total_words/2:
        print i
        break