Partitions

from functools import reduce

def part(n):
    products = sorted(product(p) for p in partitions(n))
    values = products[-1] - 1, sum(products) / len(products), sorted_median(products)
    return "Range: {} Average: {:.2f} Median {:.2f}".format(*values)

def product(arr):
    return reduce(int.__mul__, arr)

def is_prime(n):
    d = 2
    while d * d <= n:
        if n % d == 0: return False
        d += 1
    return True

def sorted_median(arr):
    return (arr[(len(arr) - 1) // 2] + arr[len(arr) // 2]) / 2

def prime_at_least(n):
    while not is_prime(n): n += 1
    return n

def partitions(n):
    current = [1] * n
    while current:
        yield current
        current = next_partition(current)

def next_partition(partition):
    if len(partition) < 2: return None

    suffix_total = sum(partition[-2:])
    new_repeated_value = prime_at_least(partition[-2] + 1)
    repetitions = suffix_total // new_repeated_value - 1
    result = partition[:-2] + [new_repeated_value] * repetitions
    result.append(suffix_total - repetitions * new_repeated_value)
    return result if is_prime(result[-1]) else next_partition(result)

n = int(input())
print(part(n))