T = int(input())
PL = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,37]
fmin = 10 ** 18
N = [int(input()) for _ in range(T)]

for n2 in N:
    n = n2
    dic = {}
    for p in PL:
        cnt = 0
        while n % p == 0:
            n //= p
            cnt += 1
        if cnt == 0:
            # 素因数に含まれない最小の素数
            fmin = p
            break
        #dic[0].remove(p)
        if cnt in dic:
            dic[cnt].add(p)
        else:
            dic[cnt] = {p}

    # 素因数の数が1の最小の素数の2乗
    if 1 in dic:
        fmin = min(fmin, min(dic[1]) ** 2)
    # 素因数の数が2の最小の素数の3乗
    if 2 in dic:
        fmin = min(fmin, min(dic[2]) ** 3)
    # 素因数の数が3の最小の素数の4乗
    if 3 in dic:
        fmin = min(fmin, min(dic[3]) ** 4)
    # 素因数の数が3の最小の素数の4乗
    if 4 in dic:
        fmin = min(fmin, min(dic[4]) ** 5)
    # 素因数の数が1の最小の素数と素因数の数が2の最小の素数の積
    if 1 in dic and 2 in dic:
        fmin = min(fmin, min(dic[1]) * min(dic[2]))
    # 素因数の数が2の最小の素数と素因数の数が3の最小の素数の積
    if 2 in dic and 3 in dic:
        fmin = min(fmin, min(dic[2]) * min(dic[3]) ** 2)
    # 素因数の数が2の最小の素数と素因数の数が3の最小の素数の積
    if 3 in dic and 4 in dic:
        fmin = min(fmin, min(dic[3]) * min(dic[4]) ** 3)
    print(fmin * n2)