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

def crivo(numero, primos):
	
	for i in xrange(2, numero):
		
		if primos[i]:
			
			for j in xrange(2 * i, numero , i):

				primos[j] = False


x = int(raw_input())

numeros = raw_input().split()

maximo = 1000010
primos = [True] * maximo
crivo(maximo, primos)

for i in xrange(x):
	
	numero = int(numeros[i])
	raiz = math.sqrt(numero)

	if numero == 1:
		
		print "NO"
	
	elif raiz == int(raiz):
		
		if primos[int(raiz)]:
			
			print "YES"
		
		else:
			
			print "NO"
	
	else:
		
		print "NO"