def f(x, p):
    res = 0
    while x % p == 0:
        x //= p
        res += 1

    return res


def solve():
    X = int(input())
    if X == 1:
        return 2

    ps = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
    exps = [[0] * len(ps) for _ in range(32)]
    for i in range(2, 32):
        x = i
        for j, p in enumerate(ps):
            while x % p == 0:
                exps[i][j] += 1
                x //= p

    res = INF
    # X に含まれない素数を掛ける
    for p in ps:
        if X % p != 0:
            res = min(res, X * p)
            break

    x_exps = [0] * len(ps)
    x = X
    for i, p in enumerate(ps):
        while x % p == 0:
            x_exps[i] += 1
            x //= p

    # X に含まれる素数も掛ける
    for i in range(2, 32): # i を掛ける
        # i を掛けたとき、約数の個数の比率はどう変化するか
        a = 1
        b = 1
        for j in range(len(ps)):
            if exps[i][j] == 0: continue
            a *= x_exps[j] + 1 + exps[i][j]
            b *= x_exps[j] + 1

        if a == b * 2:
            res = min(res, i * X)
            break

    return res


INF = 1 << 60
T = int(input())
for _ in range(T):
    ans = solve()
    print(ans)