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:
import math

prime = [True for i in range(1000000+1)]

def SieveOfEratosthenes(n):

	p = 2
	while (p * p <= n):	
		if (prime[p] == True): 
			for i in range(p * p, n+1, p): 
				prime[i] = False
		p += 1



n = int(input())
arr = [int(x) for x in input().split()]
maximum = -1
for i in range(0,n):
	if arr[i]>maximum:
		maximum = arr[i]

maximum = int(math.sqrt(maximum+1))
SieveOfEratosthenes(maximum)
for i in range(0,n):
	s = int(math.sqrt(arr[i]))
	if s*s==arr[i] and prime[s]==True and s!=1:
		print("YES")
	else:
		print("NO")