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
# file = open("input", "r")
def getIn():
	# return file.readline().strip()
	return input().strip()

def SieveOfEratosthenes(n): 
	prime = [True for i in range(n + 1)] 
	p = 2
	while (p * p <= n): 
		# If prime[p] is not changed, then it is a prime 
		if (prime[p] == True): 
			# Update all multiples of p 
			for i in range(p * 2, n + 1, p): 
				prime[i] = False
		p += 1
	prime[0]= False
	prime[1]= False
	return prime

n = int(getIn())
b = list(map(int, getIn().split(" ")))
prime = SieveOfEratosthenes(int(1e6))

for num in b:
	sr = math.sqrt(num)
	fl = math.floor(sr)
	if (sr - fl) == 0:
		if prime[int(sr)]:
			print("YES")
		else:
			print("NO")
	else:
		print("NO")