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:
'''input
4
4 5 6 9
'''
import math
from sys import stdin, stdout


def get_it():
	seive = [True] * (10 ** 6 + 1)
	for i in range(2, 10** 3 + 1):
		if seive[i] == True:
			j = i * i
			while j < 10 ** 6 + 1:
				seive[j] = False
				j += i

	p_square = set()

	for i in range(2, len(seive)):
		if seive[i] == True:
			p_square.add(i * i)
	return p_square





n = int(stdin.readline().strip())
arr = list(map(int,stdin.readline().split()))
p_square = get_it()
for i in range(n):
	if arr[i] in p_square:
		print("YES")
	else:
		print("NO")