'''
n = p1^k1 * p2^k2 * ... * pn^kn
then the diffrent solve number is ((2k1+1)(2k2+1)...(2kn+1)) / 2
'''
import math
from functools import reduce
from tools import number_theory

def updateList(limit, lst):
    lst[0] = int(limit / reduce(lambda x, y: x * (2 * y + 1), lst[1:], 1) - 0.5) + 1
    lst[0] = max(lst[:2])

def genList(limit, size):
    result = []
    base = [0] + [1] * (size - 1)
    while True:
        updateList(limit, base)
        result.append(tuple(base))
        if len(set(base)) == 1:
            break
        for i in range(1, size):
            if base[i] < base[0]:
                base[:i + 1] = [base[i] + 1] * (i + 1)
                break
    return result

def search(limit):
    size_max = int(math.log2(limit))
    prime = list(number_theory.make_prime(size_max * 2))
    mini = 2 ** limit
    for size in range(2, size_max):
        mini = min(mini, min(
                map(lambda x: reduce(lambda x, y: x * (y[0] ** y[1]),
                    zip(prime, x), 1),
                    genList(limit, size)
                )))
    return mini

print(search(1000))