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 sys,math
from collections import deque,defaultdict
import operator as op
from functools import reduce
from itertools import permutations

#sys.setrecursionlimit(10**6) 

I=sys.stdin.readline

#alpha="abcdefghijklmnopqrstuvwxyz"

"""
x_move=[-1,0,1,0,-1,1,1,-1]
y_move=[0,1,0,-1,1,1,-1,-1]
"""
def ii():
	return int(I().strip())
def li():
	return list(map(int,I().strip().split()))
def mi():
	return map(int,I().strip().split())

"""def ncr(n, r):
    r = min(r, n-r)
    numer = (reduce(op.mul, range(n, n-r, -1), 1))%(10**9+7)
    denom = (reduce(op.mul, range(1, r+1), 1))%(10**9+7)
    return (numer // denom)%(10**9+7)"""
def ncr(n, r, p):
    # initialize numerator
    # and denominator
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den, 
            p - 2, p)) % p
 

def gcd(x, y):
    while y:
        x, y = y, x % y
    return x

def valid(row,col,rows,cols,rcross,lcross):
 	return rows[row]==0 and cols[col]==0 and rcross[col+row]==0 and lcross[col-row]==0


def div(n):
	if n==1:
		return 1
	cnt=2
	for i in range(2,int(n**.5)+1):
		if n%i==0:			
			if i!=n//i:
				cnt+=2
			else:
				cnt+=1
	return cnt

	

def isPrime(n):
	if n<=1:
		return False
	elif n<=2:
		return True
	else:
		flag=True
		for i in range(2,int(n**.5)+1):
			if n%i==0:
				flag=False
				break
		return flag

def s(b):
	ans=[]
	while b>0:
		tmp=b%10
		ans.append(tmp)
		b=b//10
	return ans
prime=[1]*(10**6 + 1)
prime[1]=0
for i in range(2,int(10**6 + 1)):
	if prime[i]==1:
		for j in range(i*i,10**6 + 1,i):
			prime[j]=0




def main():
	n=ii()
	arr=li()
	ans=""
	for i in arr:
		x=int(math.sqrt(i))
		if x**2==i:
			if prime[x]:
				ans+="YES\n"
			else:
				ans+="NO\n"
		else:
			ans+="NO\n"
	print(ans)




		


		


			
		
	









					
		
		





		








	

	


 
	
	








	



	
		




	










	


	

	

		



		

		
		


	
	

		
	

		




		




			












			
		
			



		


	
			
						
			








	





			
		



	
			





	

























	
	
	





if __name__ == '__main__':
	main()