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 PYTHON):

Solution:
import math

cond = [True] * ((10**6)+1)
cond[0] = False
cond[1] = False


tam= int(math.ceil(math.sqrt(len(cond))))
for i in range(2,tam):
	if(cond[i]):
		for j in range(i+i, len(cond), i):
			cond[j] = False
			
num = raw_input()
num = int(num)
lista = map(int, raw_input().split(" "))

for l in lista:
	raiz = math.sqrt(l)
	if(raiz%1 == 0):
		primo = (cond[int(raiz)])
	else:
		primo = False
		
	if(primo):
		print "YES"
	else:
		print "NO"