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
prime = [True for i in range(10**6+1)]
def SieveOfEratosthenes(n): 
	p = 2
	while (p * p <= n): 
		if (prime[p] == True):
			for i in range(p * p, n+1, p): 
				prime[i] = False
		p += 1

if __name__=='__main__':
	n = input()
	inp = list(map (int,input().split()))
	SieveOfEratosthenes(int(math.sqrt(max(inp))))
	for i in range(len(inp)):
		if inp[i] == 1:
			print("NO")
			continue
		if int(math.sqrt(inp[i]))**2 == inp[i] and prime[int(math.sqrt(inp[i]))]:
			print("YES")
		else:
			print("NO")