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 = int(raw_input())

x = map(int,raw_input().split())

tenP6 = 10**6 + 1
tenP3 = 10**3

prime = [1]*tenP6

prime[0] = 0
prime[1] = 0

for num in xrange(tenP3) : 
	if prime[num] == 1 : 
		for j in xrange(num*2,tenP6,num) : 
			prime[j] = 0


for num in x : 
	numsqrt = math.sqrt(num)
	if abs(numsqrt - math.floor(numsqrt)) < 0.0000001 : 
		flr = int(math.floor(numsqrt))
		if prime[flr]  == 1: 
			print "YES"
		else : 
			print "NO"
	else :
		print "NO"