the program outputs "NONE" when running "play_again()" function

import random
secret_num = random.randint(1,10)
def game():
    guess = 5
    while guess:
        try:
            choice = int(input("Guess the number:\n>"))
        except ValueError:
            print("Error! 'Enter an integer'\n")
            continue        
        if choice == secret_num:
            print("Wow you guessed it correct the num is {}.".format(secret_num))
            break
        if choice < secret_num:
            print("Too low for the secret num")
        else:
            print("Too high for the secret num")                
        guess = guess - 1
        print("You have {} guess remaining.\n".format(guess))

def play_again():
    while True:
        again = input(print("Do you want to play again? Y/N\n"))

        if again.lower() == 'n':
            break
        elif again.lower() == 'y':
            game()
        else:
            print("Enter 'Y' to play again and 'N' to quit the game")    
game()
play_again()