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:
from math import sqrt
def get_int():
    from sys import stdin
    return int(stdin.readline().replace('\n', ''))

def get_int_list():
    from sys import stdin
    return [int(x) for x in stdin.readline().replace('\n','').split(' ')]

def isqrt(n):
    sqrt = int(n**0.5) -1
    if sqrt**2 == n:
        return sqrt
    sqrt+=1
    if sqrt**2 == n:
        return sqrt
    sqrt+=1
    if sqrt**2 == n:
        return sqrt
    return -1

def sieve_of_eratosthenes(n):  
    primes = [True for i in range(n+1)] 
    p = 2
    while (p**2 <= n):           
        if (primes[p] == True): 
            for i in range(p**2, n+1, p): 
                primes[i] = False
        p += 1
    return primes
    

def is_prime(n, primes = []):
    return primes[n] 

def is_tprime(n, sieve):
    rt = isqrt(n)
    return 'YES' if n > 1 and rt != -1 and is_prime(rt, sieve) else 'NO'


n = get_int()
_list = get_int_list()
max_list = max(_list)
sieve = sieve_of_eratosthenes(int(sqrt(max_list))+5)

for i in _list:
    print(is_tprime(i, sieve))