def solve(X):
    primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
    factor_x = [0] * len(primes)
    prod_x = 1
    x_ = X
    for i, p in enumerate(primes):
        while not x_ % p:
            x_ //= p
            factor_x[i] += 1
        prod_x *= factor_x[i] + 1
    for n in range(2, 32):
        factor_y = factor_x.copy()
        prod_y = 1
        for i, p in enumerate(primes):
            n_ = n
            while not n_ % p:
                n_ //= p
                factor_y[i] += 1
            prod_y *= factor_y[i] + 1
        if prod_x * 2 == prod_y:
            return X * n
    return -1


T = int(input())
for _ in range(T):
    print(solve(int(input())))