""" Coin sums Problem 31: https://projecteuler.net/problem=31 In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p). It is possible to make £2 in the following way: 1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p How many different ways can £2 be made using any number of coins? """ def one_pence() -> int: return 1 def two_pence(x: int) -> int: return 0 if x < 0 else two_pence(x - 2) + one_pence() def five_pence(x: int) -> int: return 0 if x < 0 else five_pence(x - 5) + two_pence(x) def ten_pence(x: int) -> int: return 0 if x < 0 else ten_pence(x - 10) + five_pence(x) def twenty_pence(x: int) -> int: return 0 if x < 0 else twenty_pence(x - 20) + ten_pence(x) def fifty_pence(x: int) -> int: return 0 if x < 0 else fifty_pence(x - 50) + twenty_pence(x) def one_pound(x: int) -> int: return 0 if x < 0 else one_pound(x - 100) + fifty_pence(x) def two_pound(x: int) -> int: return 0 if x < 0 else two_pound(x - 200) + one_pound(x) def solution(n: int = 200) -> int: """Returns the number of different ways can n pence be made using any number of coins? >>> solution(500) 6295434 >>> solution(200) 73682 >>> solution(50) 451 >>> solution(10) 11 """ return two_pound(n) if __name__ == "__main__": print(solution(int(input().strip())))