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 generate(n):
	prime=[True for i in range(n+1)]
	p=2
	while(p*p<=n):
		if(prime[p]==True):
			for j in range(p*p,n+1,p):
				prime[j]=False
		p=p+1
	return prime
	#l=[]
	'''for k in range(2,n+1):
		if(prime[k]==True):
			#print(k)
			l.append(k)
	return l'''

limit=pow(10,6)
ok=generate(limit)
#print(ok[:5])
n=int(input())
a=list(map(int,input().split()))
ans=[]
for i in a:
	z=int(pow(i,.5))
	if z*z == i and z!=1:
		if ok[z]==True:
			print('YES')
		else:
			print('NO')
	else:
		print('NO')