import math
import sympy.ntheory as spn

powers = {}
powers[2] = 39
powers[3] = 19
powers[5] = 9
powers[7] = 6
powers[11] = 3
powers[13] = 3
powers[17] = 2
powers[19] = 2
powers[23] = 1
powers[29] = 1
powers[31] = 1
powers[37] = 1
powers[41] = 1
powers[43] = 1

limit = math.factorial(43)
primes = sorted(list(powers.keys()))

allProds = set()
memo = {}
print(limit)

def findC(ab):
    tp = tuple()
    res = 1
    for p in primes:
        i = 1
        while ab % pow(p,i) == 0:
            i += 1
        i -= 1
        if i > powers[p]: return 0
        tp = tp + (powers[p]-i,)
    for i in range(len(primes)):
        res *= pow(primes[i], tp[i])
    return res

def bfs(currTpls, ind, lastProd):
    if ind == len(primes): return
    print(ind, len(allProds), len(currTpls))
    newTpls = []
    p = primes[ind]
    for tp in currTpls:
        if pow(tp*lastProd,3) >= limit - int(pow(10,15)):
            for i in range(powers[p]+1):
                if pow(tp * pow(p,i)-pow(10,13),3) <= limit:
                    newTpls.append(tp*pow(p, i))
                    if pow(tp*pow(p,i)+pow(10,13),3) >= limit:
                        allProds.add(tp*pow(p,i))
                else:
                    break
        else:
            break
    newTpls = sorted(newTpls, reverse=True)
    return bfs(newTpls, ind+1, lastProd//pow(p,powers[p]))

currTpls = []
for i in range(powers[2]+1):
    memo[pow(2,i)] = (i)
    currTpls.append(pow(2,i))

bfs(currTpls, 1, limit//pow(2,powers[2]))
print(len(allProds))

allProdsList = list(allProds)
allProdsList.sort()

minRatio = 10000
minTp = []
for i in range(len(allProdsList)):
    a = allProdsList[i]
    for j in range(i, len(allProdsList)):
        b = allProdsList[j]
        c = findC(a*b)
        if b <= c:
            if c/a < minRatio:
                minTp = [a,b,c]
                minRatio = c/a
    print(i, minRatio, minTp)

print(minRatio)
print(minTp)
print(sum(minTp))
print(limit, a*b*c)