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
n=10**6
def cuad(n):
	if n==1:
		return False
	if math.sqrt(n)%1==0:
		return True
	return False
esprimo=[True]*(n+1)
for i in range (2,n+1):
        if esprimo[i]:
                for j in range(i*i,n+1,i):
                        esprimo[j]=False 
def tprimo(i):
	if cuad(i):
		if esprimo[int(math.sqrt(i))]:
			print "YES"		
		else:
			print "NO"
	else:
		print "NO"
z=input()
x = [int(x) for x in raw_input().split()]
for i in x:
	tprimo(i)