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:
from sys import *
from math import *

maxn = 10 ** 6 + 5

isprime = [True] * maxn

def sieve():
	isprime[0] = isprime[1] = False
	for i in range(4, maxn, 2): isprime[i] = False
	for i in range(3, maxn, 2):
		if i * i >= maxn: break
		if isprime[i] is True:
			for j in range(i * i, maxn, i + i): isprime[j] = False
				
sieve()
n = int(stdin.readline())
arr = list(map(int, stdin.readline().split()))
for x in arr:
	sq = int(sqrt(x * 1.0))
	ok = False
	if sq * sq is x and isprime[sq] is True: ok = True
	print("YES" if ok is True else "NO")