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:
import java.io.*;
import java.lang.*;
import java.util.*;

public class Main
{
	static class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 
  		
		public FastReader() 
		{ 
			br = new BufferedReader ( new InputStreamReader(System.in) ); 
		}
  
		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException  e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 
  
		int nextInt() 
		{ 
			return Integer.parseInt(next()); 
		} 
  
		long nextLong() 
		{ 
			return Long.parseLong(next()); 
		} 
  
		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 
  
		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	} 
  
	public static void main(String args[])throws IOException
	{

		FastReader r = new FastReader();
		final int MAX = 1000001;
		boolean[] isPrime = new boolean[MAX];
		for(int i = 0; i < isPrime.length; i++)
			isPrime[i] = true;

		isPrime[0]=false;
		isPrime[1] =false;

		for(long i =2; i < isPrime.length; i ++)
		{
			if(!isPrime[(int)i])
				continue;
			for(long j = i*i ; j < isPrime.length; j = j + i)
			{
				isPrime[(int)j] = false;
			}
		}

		int N = r.nextInt();

		boolean result = false;
		for(int i = 0; i < N; i++)
		{
			long T = r.nextLong();
			if(isPerfectSquare(T) && isPrime[squareRoot(T)])
			{
				System.out.println("YES");
			}
			else
			{
				System.out.println("NO");
			}
		}
	}

	public static boolean isPerfectSquare(long x)
	{
		double sqrt = Math.sqrt(x);
		return (sqrt - Math.floor(sqrt) )== 0; 
	}

	public static int squareRoot(long x)
	{
		double s  =Math.sqrt(x);
		return (int)(Math.floor(s));
	}
}