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 JAVA):

Solution:
public class Main {
	public static void main(String[] args){ 
		java.util.Scanner input = new java.util.Scanner(System.in);
		String ans = "YES";
		boolean [] isCompositeOdd = new boolean[499999];
	    for(int n = 0 ; n*n < 500000 ; n++)
	    	if(!isCompositeOdd[n])
	    		for(int counter = 4*n*n+12*n+9 ; counter < 1000000 ; counter += 4*n+6)
	    			isCompositeOdd[counter-3 >> 1] = true;
		int t = input.nextInt();
		for(int count = 0 ; count < t ; count++)
		{
			double target = Math.sqrt(input.nextLong());
			if(target == 2)
				ans="YES";
			else	
			if(target%1 != 0 || target%2 == 0 || target < 3)
			   ans = "NO";
			else
			if(!isCompositeOdd[(int)(target)-3 >>1])
				ans = "YES";
			else
				ans = "NO";	
			System.out.println(ans);
		}	
	}
	/*static boolean isPrime(double number)
	{
		if(number == 2)
			return true;
		if(number%1 != 0 || number%2 == 0 || number == 1)
			return false;
		for(int count = 3 ; count*count <= number ; count+=2)
			if(number%count == 0)
				return false;
		return true;
	}*/
}