#!/usr/bin/env python3

from lib import primegen
from math import log
from operator import mul
from functools import reduce

def calc(pows):
    return (reduce(mul, (2*p + 1 for p in pows)) + 1) // 2

def increment(i, pows):
    n = 0
    if i < len(pows):
        n = pows[i]
    return [n + 1] * (i+1) + pows[i+1:]

def val(pows):
    return sum(p*v for p, v in zip(pows, vals))

def fpwof2(pows, n):
    if len(pows) == 1:
        return n-1
    r = (2*n - 1) // reduce(mul, (2*p + 1 for p in pows[1:]))
    r = (r - 1) // 2
    while calc([r] + pows[1:]) < n:
        r += 1
    return r

N = 4 * 10**6

primes = list(primegen(100))
vals   = [log(p) / log(2) for p in primes]

i = 0
pows = [0]
best = fpwof2(pows, N)
best_pows = None

while not (val(pows) >= best and sum(pows) == len(pows)):
    if not i:
        pows[0] = fpwof2(pows, N)
        if len(pows) > 1 and pows[0] < pows[1]:
            pows[0]  = pows[1]
        if val(pows) < best:
            best = val(pows)
            best_pows = pows
        i = 1
    pows = increment(i, pows)
    if val(pows) >= best:
        i += 1
    else:
        i = 0

print(reduce(mul, (n**pw for n, pw in zip(primes, best_pows))))