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 prime(n):
	arr = [True]*(n+1)
	arr[0] = arr[1] = False
	for i in range(2,int((n+1)**0.5)):
		if arr[i]==True:
			for j in range(2*i,n+1,i):
				arr[j] = False
	return arr

n = int(input())
arr = [int(x) for x in input().strip().split()]
prime = prime(10**6)
def is_int(n):
	k = float(int(n))
	if k!=n:
		return False
	return True
for i in arr:
	x = i**0.5
	if is_int(x) and prime[int(x)]:
		print("YES")
	else:
		print("NO")