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 crive(listt, ln):
	for k in xrange(2, ln, 1):
		if listt[k]:
			w = k**2
			while w < ln:
				listt[w] = False
				w += k
	return listt
	
MAX = 1000001
prime_or_not = [False, False] + MAX * [True]
primes = crive(prime_or_not, MAX)

n = int(raw_input())
listt = map(int, raw_input().split())
for i in listt:
	sqrt_d = math.sqrt(i)
	sqrt_l = long(sqrt_d)
	diff = sqrt_d - sqrt_l

	if (diff == 0) and primes[sqrt_l]:
		print "YES"
	else:
		print "NO"