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 primes(n):
	p = [True] * (n + 1)
	p[0] = p[1] = False
	i = 4
	while i <= n:
		p[i] = False
		i += 2
	i = 3
	while i * i <= n:
		if p[i]:
			j = i * i
			while j <= n:
				p[j] = False
				j += i
		i += 2
	return p

p = primes(10 ** 6)
n = int(input())
for i in map(int, input().split()):
	x = int(i ** 0.5)
	ans = (i**0.5) - x < 1e-10 and p[x]
	print(['NO', 'YES'][ans])