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:
import math
from collections import defaultdict, Counter, deque

INF = float('inf')

def gcd(a, b):
	while b:
		a, b = b, a%b
	return a

def isPrime(n):
	if (n <= 1): 
		return False
	i = 2
	while i ** 2 <= n:
		if n % i == 0:
			return False
		i += 1
	return True

def primeFactor(n):
	if n % 2 == 0:
		return 2
	i = 3
	while (i ** 2) <= n:
		if n % i == 0:
			return i 
		i += 1
	return n

def vars():
	return map(int, input().split())

def array():
	return list(map(int, input().split()))

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

	arr = array()

	for num in arr:
		if int(num ** 0.5) ** 2 == num:
			if isPrime(int(num ** 0.5)):
				print('YES')
			else:
				print("NO")
		else:
			print('NO')
	


if __name__ == "__main__":
	# t = int(input())
	t = 1
	for _ in range(t):
		main()