#ulam.py
#Ulam's recursive function

def ulam(n, yes_print=True):
    if yes_print:
        print(n, end=" ")
    if n == 1:
        return 1
    elif n%2 == 0:   #n even, call again with half of n
        return ulam(n // 2, yes_print) + 1  #avoid float .
    else:            #n odd, call again with 3n+1
        return ulam(3*n+1, yes_print) + 1
'''
ulam(5)
print()
ulam(12)
print()
ulam(97)
print()
'''
end_int = int(input("Ending int to go up to: "))
num_recurses = [0]  #one item
for i in range(1,end_int+1):
#    print(i,": ", end="")
    num_recurses.append(ulam(i,yes_print=False))
#    print(num_recurses[i], end=" ")

max_calls = max(num_recurses)
print("Max calls: ", max_calls)
print("   number is", num_recurses.index(max_calls), "(might be dups)")
print("Average:",(sum(num_recurses)/len(num_recurses)))

'''
N        avg    max
100       32    119
1000      60    179
10000     85    262
100000   108    351
1000000  132    525
'''