Problem: We know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we'll call a positive integer t Т-prime, if t has exactly three distinct positive divisors.

You are given an array of n positive integers. For each of them determine whether it is Т-prime or not.

Input

The first line contains a single positive integer, n (1 ≤ n ≤ 105), showing how many numbers are in the array. The next line contains n space-separated integers xi (1 ≤ xi ≤ 1012).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.

Output

Print n lines: the i-th line should contain "YES" (without the quotes), if number xi is Т-prime, and "NO" (without the quotes), if it isn't.

Examples

Input

3
4 5 6


Output

YES
NO
NO

Note

The given test has three numbers. The first number 4 has exactly three divisors — 1, 2 and 4, thus the answer for this number is "YES". The second number 5 has two divisors (1 and 5), and the third number 6 has four divisors (1, 2, 3, 6), hence the answer for them is "NO".

Solution (in PYTHON):

Solution:
def gera_primos():
    limite = 1000000

    primos = [True] * limite
    primos[0] = primos[1] = False

    for i in range(2, limite):
        if primos[i]:
            for j in range(i*i, limite, i):
                primos[j] = False

    return primos


def t_prime(n, primos):
    if n == 4:
        return True

    if n < 4 or n % 2 == 0:
        return False

    sqrt_n = n ** 0.5

    if (sqrt_n == int(sqrt_n)) and (primos[int(sqrt_n)]):
        return True

    return False


def main():
    primos = gera_primos()

    q = int(input())

    numbers = raw_input().split(" ")
    numbers = [int(num) for num in numbers]

    for i in numbers:
        if t_prime(i, primos):
            print("YES")
        else:
            print("NO")


main()