from functools import lru_cache

def f(n):

cisla = []

for k in range(2, n + 1):

if n % k == 0:

cisla.append(n + n // k)

return cisla

@lru_cache

def game(n):

if any(x > 45 for x in f(n)):

return 'vic'

if all (game(x)=='vic' for x in f(n)):

return 'loss1'

if any (game(x)=='loss1' for x in f(n)):

return 'vic2'

if all (game(x)=='vic' or game(x) == 'vic2' for x in f(n)):

return 'loss2'

z_19 = []

z_20 = []

z_21 = []

for n in range(2,46):

if game(n) =='loss1':

z_19.append(n)

if game(n) =='vic2':

z_20.append(n)

if game(n) =='loss2':

z_21.append(n)

print(len(z_19))

print(min(z_20), max(z_20))

print(min(z_21))

def f(x, z):

if x > 45: return z%2==0

if z == 0: return 0

h = [f(x + x//i, z-1) for i in range(2, x+1) if x % i == 0]

if (z-1)%2==0:

return any(h)

return all(h)

print(19, len([s for s in range(2, 45) if f(s, 2)]))

print(20, [s for s in range(1, 45) if (not f(s, 1)) and f(s, 3)])

print(21, [s for s in range(1, 45) if ((f(s, 2)) or f(s, 4)) and (not f(s, 2))])

from functools import lru_cache

def f(n):

cisla = []

for k in range(2, n + 1):

if n % k == 0:

cisla.append(n + n // k)

return cisla

@lru_cache

def game(n):

if any(x > 45 for x in f(n)):

return 'vic'

if all (game(x)=='vic' for x in f(n)):

return 'loss1'

if any (game(x)=='loss1' for x in f(n)):

return 'vic2'

if all (game(x)=='vic' or game(x) == 'vic2' for x in f(n)):

return 'loss2'

z_19 = []

z_20 = []

z_21 = []

for n in range(2,45):

if game(n) =='loss1':

z_19.append(n)

if game(n) =='vic2':

z_20.append(n)

if game(n) =='loss2':

z_21.append(n)

print(len(z_19))

print(min(z_20), max(z_20))

print(min(z_21))

def f(x, z):

if x > 45: return z%2==0

if z == 0: return 0

h = [f(x + x//i, z-1) for i in range(2, x+1) if x % i == 0]

if (z-1)%2==0:

return any(h)

return all(h)

print(19, len([s for s in range(2, 45) if f(s, 2)]))

print(20, [s for s in range(1, 45) if (not f(s, 1)) and f(s, 3)])

print(21, [s for s in range(1, 45) if ((f(s, 2)) or f(s, 4)) and (not f(s, 2))])

from functools import lru_cache

def f(n):

cisla = []

for k in range(2, n + 1):

if n % k == 0:

cisla.append(n + n // k)

return cisla

@lru_cache

def game(n):

if any(x > 40 for x in f(n)):

return 'vic'

if all (game(x)=='vic' for x in f(n)):

return 'loss1'

if any (game(x)=='loss1' for x in f(n)):

return 'vic2'

if all (game(x)=='vic' or game(x) == 'vic2' for x in f(n)):

return 'loss2'

z_19 = []

z_20 = []

z_21 = []

for n in range(2,40):

if game(n) =='loss1':

z_19.append(n)

if game(n) =='vic2':

z_20.append(n)

if game(n) =='loss2':

z_21.append(n)

print(len(z_19))

print(min(z_20), max(z_20))

print(max(z_21))

from functools import lru_cache

def f(n):

cisla = []

for k in range(2, n + 1):

if n % k == 0:

cisla.append(n + n // k)

return cisla

@lru_cache

def game(n):

if any(x > 40 for x in f(n)):

return 'vic'

if all (game(x)=='vic' for x in f(n)):

return 'loss1'

if any (game(x)=='loss1' for x in f(n)):

return 'vic2'

if all (game(x)=='vic' or game(x) == 'vic2' for x in f(n)):

return 'loss2'

z_19 = []

z_20 = []

z_21 = []

for n in range(2,40):

if game(n) =='loss1':

z_19.append(n)

if game(n) =='vic2':

z_20.append(n)

if game(n) =='loss2':

z_21.append(n)

print(len(z_19))

print(min(z_20), max(z_20))

print(max(z_21))