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:
#n, m = map(int, input().strip().split())
import math
n=int(input())


arr = list(map(int, input().strip().split()))

 
    # Create a boolean array
    # "prime[0..n]" and initialize
    #  all entries it as true.
    # A value in prime[i] will
    # finally be false if i is
    # Not a prime, else true.
    
prime = [True for i in range(1000000+1)]
p = 2
while (p * p <= 1000000):
	if prime[p]==True:
		for i in range(p*p,1000000+1,p):
			prime[i]=False
	p+=1
		
	
	
	
    
	
 
        # If prime[p] is not
        # changed, then it is a prime
        
 
def isPerfectSquare(n):
 
    #if x >= 0,
        if (math.ceil(math.sqrt(n)) ==math.floor(math.sqrt(n))):
        	return True
        else:
        	return False
for i in arr:
	if i<4:
		print("NO")
		continue
	
	
	if i==4:
		print("YES")
		continue
	
	elif i%2==1 and isPerfectSquare(i):
		sr=math.sqrt(i)
		sr=int(sr)
		
		if prime[sr]:
		
		
			print("YES")
		else:
			print("NO")
	else:
		print("NO")