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:

   # while True:
    #    try:
     #       n = int(input())
      #  except EOFError:
        #    break
        #x,y = nth_prime_number(n*2)
from functools import reduce
import math  
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))

def invr():
    return(map(int,input().split()))
    
def loadinput():
    n = int(input())
    nums = list(map(int,input().split()))
    return n,nums
def primes1(n):
    """ Returns  a list of primes < n """
    sieve = [True] * (n//2)
    for i in range(3,int(n**0.5)+1,2):
        if sieve[i//2]:
            sieve[i*i//2::i] = [False] * ((n-i*i-1)//(2*i)+1)
    return  [2]+ [2*i+1 for i in range(1,n//2) if sieve[i]] 
def is_prime(n):
    if n == 2:
        return True
    if n <= 1:
        return False
    sqr = int(math.sqrt(n)) + 1
    for divisor in range(3, sqr, 2):
        if n % divisor == 0:
            return False
    return True
limit = 1000000
def calculate_prime_flag_for_each_number_upto_limit():
    prime_flag = [True] * limit
    prime_flag[0] = prime_flag[1] = False
    for i in range(2,limit):
        if prime_flag[i] == True:
            for j in range(i*i, limit, i):
                prime_flag[j] = False
    return prime_flag     

def factors(n):    
    return set(reduce(list.__add__, 
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
def check_if_a_number_is_t_prime(n):
    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):
        if prime_flag[int(sqrt_n)] == True:
            return True
    return False

if __name__ == '__main__':
    prime_flag = calculate_prime_flag_for_each_number_upto_limit()
    k, nums = loadinput()
    for n in nums:  
        if check_if_a_number_is_t_prime(n):    
            print('YES')
        else:
            print('NO')

   # n,nums = 
    #for _ in nums: