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:
def fastio():
	import sys
	from io import StringIO 
	from atexit import register
	global input
	sys.stdin = StringIO(sys.stdin.read())
	input = lambda : sys.stdin.readline().rstrip('\r\n')
	sys.stdout = StringIO()
	register(lambda : sys.__stdout__.write(sys.stdout.getvalue()))
fastio()

MOD = 10**9 + 7
I = lambda:list(map(int,input().split()))

p = [1]*(1000001)
p[0] = p[1] = 0
for i in range(2, 1000001):
	if p[i]:
		for j in range(2*i, 1000001, i):
			p[j] = 0

n, = I()
l = I()
for i in l:
	if i**0.5 == int(i**0.5) and p[int(i**0.5)]:
		print("YES")
	else:
		print('NO')