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:
import math

n = int(input())

xs = [int(x) for x in input().split()]

mx = max(xs)

r = int(math.sqrt(mx))

sieve = [True] * (r+1)

sieve[0] = False
sieve[1] = False

if r >= 2:
	for i in range(2, r//2 + 1):
		sieve[i * 2] = False

if r >= 3:
	for i in range(2, r//3 + 1):
		sieve[i * 3] = False

if r >= 5:
	for i in range(5, r+1, 2):
		if sieve[i]:
			for j in range(2*i, r+1, i):
				sieve[j] = False

for x in xs:
	root = int(math.sqrt(x))
	if root * root == x and sieve[root]:
		print('YES')
	else:
		print('NO')