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:
import math
from fractions import gcd

prime_mult = 2
primes = [2]

def is_prime(num):
    if num > primes[-1]:
        return gcd(num, prime_mult) == 1
    else:
        return num in primes

if __name__ == "__main__":
    n = int(raw_input())
    nums = map(int, raw_input().split())
    for i in range(2, 1001):
        if is_prime(i):
            prime_mult *= i
            primes.append(i)
    for num in nums:
        sqrt = int(math.sqrt(num))
        if num > 1 and sqrt ** 2 == num and is_prime(sqrt):
            print "YES"
        else:
            print "NO"