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:
from math import sqrt

def primes(m):
	p = []
	for i in xrange(0, m):
		if (i < 2):
			p.append(False)
		else:
			p.append(True)
	b = int(sqrt(m))
	for i in xrange(0, b + 1):	
		if (p[i]):
			for j in xrange (i * i, m, i):
				p[j] = False
	return p
	

n = int(raw_input())
a = map(int, raw_input().split())
res = ""
p = primes(1000001)
for x in a:
	k = int(sqrt(x))
	if (k * k == x) and p[k]:
		res += "YES\n"
	else:
		res += "NO\n"
		
print res