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"""
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.")