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 random, math
from copy import deepcopy as dc

# To Genrate Random Number for Test-Cases
def randomNumber(s, e):
	return random.randint(s, e)

# To Generate Random Array for Test-Cases
def randomArray(s, e, s_size, e_size):
	size = random.randint(s_size, e_size)
	arr = [randomNumber(s, e) for i in range(size)]
	return arr

# To Generate Question Specific Test-Cases
def testcase():
	pass

# Brute Force Approach to check Solution
def brute():
	pass

# Efficient Approach for problem
def effe():
	pass
MAXN = (10**6 + 1)
primes = [1] * MAXN
primes[0] = 0
primes[1] = 0

# Function for generating seive
def seive():
	i = 2
	while i*i <= MAXN:
		if primes[i]:
			for j in range(i*i, MAXN, i):
				primes[j] = 0
		i += 1




# Function to call the actual solution
def solution(num):
	if num == 1:
		return "NO"
	sq = int(num ** 0.5)
	if sq * sq == num and primes[sq]:
		return "YES"
	return "NO"



# Function to take input
def input_test():
	n = int(input())
	li = list(map(int, input().strip().split(" ")))
	for i in li:
		out = solution(i)
		print(out)


# Function to check test my code
def test():
	pass

seive()
input_test()
# test()