import os
import sys
from memoized import memoized
import numpy
from fractions import Fraction

INIT_VAL = 60
CAPS = {}

def series_value(*vals):
    tot_den = 0
    for v in vals: tot_den = tot_den + Fraction(1, v)
    return Fraction(1, tot_den)

def par_value(*vals):
    return sum(vals)

all_forms = set()

@memoized
def add_forms2(f1, f2):
    forms = set()
    for one_f in f1:
        for two_f in f2:
            forms.add(series_value(one_f, two_f))
            forms.add(par_value(one_f, two_f))
    forms = forms - all_forms
    all_forms.update(forms)
    return forms

def add_forms(f1, f2):
    if len(f1) < len(f2):
        first = f1
        second = f2
    else:
        first = f2
        second = f1

    return add_forms2(tuple(first), tuple(second))

@memoized
def cap_forms(num_caps):
    if num_caps == 1:
        all_forms.add(INIT_VAL)
        return [INIT_VAL]

    num_set1 = 1
    forms = set()

    while num_set1 < num_caps:
        num_set2 = num_caps - num_set1
        f1 = cap_forms(num_set1)
        #print num_caps,num_set1,sorted(f1)
        f2 = cap_forms(num_set2)
        #print num_caps,num_set2,sorted(f2)

        forms.update(add_forms(f1, f2))
        num_set1 += 1

    print "Returning for num_caps %d = %d" % (num_caps,len(forms))
    #print sorted(forms)
    return list(forms)

def cap_forms_fast(num_caps):
    if num_caps > 3:
        return 3*cap_forms_fast(num_caps-1) - 2*cap_forms_fast(num_caps-2)
    elif num_caps == 3:
        return 7
    elif num_caps == 2:
        return 3
    else:
        return 1

def main():
    if len(sys.argv) <= 1:
        print len(cap_forms(10))
    else:
        print len(cap_forms(int(sys.argv[1])))
    print len(all_forms)
    #print sorted(all_forms)
    #print cap_forms_fast(10)

if __name__ == "__main__":
    sys.exit(main())