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
class Main:
	l=[0]*1000001
	l[1]=1
	for i in range(2,1000):
		if l[i]==0:
			j=i*i
			while(j<1000001):
				l[j]=1
				j+=i
		
	t=int(input())
	s=raw_input().split(" ")
	l1=[int(x) for x in s]
	for i in l1:
#		if(i==1):
#			print "NO"
#		else:
		n=math.sqrt(i)
		m=int(n)
		if(n==m):
			if(l[m]==0):
				print "YES"
			else:
				print "NO"
#			j=math.sqrt(n)
#				k=2
#				while(k<=j):
#					if(n%k==0):
#						print "NO"
#						flag=0
#						break
#					k+=1
#				if(flag==1):
#					print "YES"
		else:
			print "NO"