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 primes_sieve(limit):
	d = {}
	limitn = limit+1
	not_prime = [False] * limitn
	primes = []
	for i in range(2, limitn):
	    if not_prime[i]:
	        continue
	    for f in xrange(i*2, limitn, i):
	        not_prime[f] = True

	    d[i] = 1

	return d

d = primes_sieve(1000000)

n = int(raw_input())
a = map(int,raw_input().split())
for i in xrange(n):
	if a[i] < 4:
		print "NO"
	else:
		val = math.sqrt(a[i])
		#print val
		if math.ceil(val) != math.floor(val):
			print "NO"
		else:
			# check if number is prime
			if int(val) in d:
				print "YES"
			else:
				print "NO"