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:
from bisect import bisect_left 
def search(a, x): 
	i = bisect_left(a, x) 
	if i != len(a) and a[i] == x: 
		return i 
	else: 
		return -1
def genPrimes(n):
	sieve = [True]*(n+1)
	p = 2
	while p*p <= n:
		if sieve[p]:
			for i in range(p*p, n+1, p):
				sieve[i] = False
		p += 1
	primes = []
	for i in range(2, n+1):
		if sieve[i]:
			primes.append(i**2)
	return primes
poss = genPrimes(1000010)
n = int(input().strip())
arr = list(map(int, input().strip().split()))
for i in arr:
	if search(poss, i) != -1:
		print("YES")
	else:
		print("NO")