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 PYTHON3):

Solution:
from math import sqrt

def perfectSquare(n):
	root = sqrt(n)
	if int(root + 0.5) ** 2 == n:
		return True, int(root + 0.5)
	else:
		return False, -1

def primes(n):
	prime = [True] * (n+1)
	p = 2
	while (p * p <= n):
		if (prime[p] == True):
			for i in range(p * p, n+1, p):
				prime[i] = False
		p += 1

	return prime

def TPrime(n):
	if n == 4:
		return True
	if n < 9:
		return False
	if n%2 == 0:
		return False
	ps, root = perfectSquare(n)
	if not ps:
		return False
	if prime[root] == False:
		return False

	return True

def main():
	t = int(input())

	tests = map(int, input().split())

	for t in tests:
		if TPrime(t):
			print("YES")
		else:
			print("NO")


if __name__ == '__main__':
	prime = primes(10**6)
	main()