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:


B=[]
n=10**6+4
prime=[True for i in range(n+1)]
p=2

while p*p<=n:
	if prime[p]==True:
		for i in range(p*p, n+1, p): 
			prime[i] = False	
	p=p+1

for p in range(2, n): 
        if prime[p]: 
            B.append(p)

def BS(B,x,l,h):
	if h>=l:
		m=(h+l)//2
		if x>B[m]:
			return BS(B,x,m+1,h)
		elif x<B[m]:
			return BS(B,x,l,m-1)
		else:
			return True
	return False

N=int(input())
A=list(map(int,input().split()))

for i in A:
	j=i**0.5
	if j==int(j) and j<1000000:
		if BS(B,j,0,len(B)): 
			print("YES")
		else:
			print("NO")
	else:
		print("NO")