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 sys
t_prime=set()
is_prime = [ True for i in range(10**6+1) ] 
is_prime[0] = is_prime[1] = False
for p in range(2,10**6+1):
	if is_prime[p]:
		t_prime.add(p**2)
		for k in range(2*p,10**6+1,p): 
			is_prime[k] = False 
			
N=int(sys.stdin.readline())
array=[int(x) for x in (sys.stdin.readline()).split()]
for i in array:
	if i in t_prime:
		print("YES")
	else:
		print("NO")