""" The number of partitions of a number n into at least k parts equals the number of partitions into exactly k parts plus the number of partitions into at least k-1 parts. Subtracting 1 from each part of a partition of n into k parts gives a partition of n-k into k parts. These two facts together are used for this algorithm. """ def partition(m): memo = [[0 for _ in range(m)] for _ in range(m + 1)] for i in range(m + 1): memo[i][0] = 1 for n in range(m + 1): for k in range(1, m): memo[n][k] += memo[n][k - 1] if n - k > 0: memo[n][k] += memo[n - k - 1][k] return memo[m][m - 1] if __name__ == "__main__": import sys if len(sys.argv) == 1: try: n = int(input("Enter a number: ").strip()) print(partition(n)) except ValueError: print("Please enter a number.") else: try: n = int(sys.argv[1]) print(partition(n)) except ValueError: print("Please pass a number.")