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 PYTHON):

Solution:
def main():
	import sys
	n = pow(10,6)
	primos = [True] * (n+1)
	primos[0] = False
	primos[1] = False

	for i in xrange(2,int(n**0.5)+1):
		
		if primos[i]:
			for j in xrange(2*i,n+1,i):
				primos[j] = False

	m = sys.stdin.readline()
	nums = sys.stdin.readline().split()

	for x in nums:
		
		x = int(x)
		x **= 0.5
		
		if x % 1 == 0:
			
			if primos[int(x)]:
				sys.stdout.write("YES\n")
			else:
				sys.stdout.write("NO\n")
		else:
			sys.stdout.write("NO\n")

if __name__ == "__main__":
	main()