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 math import sqrt
n = int(input())
l = list(map(int,input().split()))
def prime_sieve():
	arr = [True for i in range(1000003)]

	arr[1] = False
	for i in range(2,1002):
		if arr[i]:
			for k in range(2*i,1000003,i):
				arr[k] = False
	return arr
primes = prime_sieve()
#print(primes[:10])
for n in l:
	root = int(sqrt(n))
	#print(root)
	if root == 1:
		print("NO")
	elif root**2 == n:
		if primes[root]:
			print("YES")
		else:
			print("NO")
	
	elif (root+1)**2 == n:
		if primes[root+1]:
			print("YES")
		else:
			print("NO")
	else:
		print("NO")