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 PYTHON3):

Solution:
import math

def main():
    _ = int(input())
    numbers = [int(i) for i in input().split(" ")]

    for number in numbers:
        if is_t_prime(number):
            print("YES")
        else:
            print("NO")


def is_t_prime(num):
    if num < 4:
        return False
    if num > 4 and num % 2 == 0:
        return False

    # for a number to be t-prime, it needs to be a x**2, where x is prime
    sqrt_ = math.sqrt(num)
    if sqrt_ == int(sqrt_):
        if is_prime(int(sqrt_)):
            return True
    return False


def is_prime(num):
    if num <= 1:
        return False
    if num == 2 or num == 3:
        return True
    if num % 2 == 0 or num % 3 == 0:
        return False
    fact = 5
    while fact * fact <= num:
        if num % fact == 0:
            return False
        fact += 2
    return True

if __name__ == "__main__":
    main()