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:
primes = [2,3,5,7,11,13,17]
int(input())
x = list(map(int, input().split()))
for i in x:
	t = i**(.5)
	if t == int(t) and i != 1:
		t = int(t)
		for j in primes:
			if t==j:
				print('YES') 
				break
			elif t%j == 0:
				print('NO')
				break
		else:
			for j in range(primes[-1]+1, int(t**(.5)) + 1):
				for k in primes:
					if j%k == 0: break
				else:
					primes.append(j)
					if t % j == 0: 
						print('NO')
						break
			else: print('YES')
	else: print('NO')