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.util.*;
	
	public class practice {
		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; 
	        } 
	    } 
		static class Print
		{
		    private final BufferedWriter bw;
		    public Print()
		    {
		        bw=new BufferedWriter(new OutputStreamWriter(System.out));
		    }
		    public void print(String str)throws IOException
		    {
		        bw.append(str);
		    }
		    public void println(String str)throws IOException
		    {
		        print(str);
		        bw.append("\n");
		    }
		    public void close()throws IOException
		    {
		        bw.close();
		    }}
			public static void main(String[] args) throws IOException {			
				FastReader scn=new FastReader();
				Print p=new Print();
				boolean[] pre=new boolean[1000005];
				Arrays.fill(pre,true);
				for(int i=2;i*i<=1000004;i++){
					if(pre[i]==true){
						for(int j=i*i;j<=1000004;j+=i){
							pre[j]=false;
						}
					}
				}
				long n=scn.nextLong();
				double root1=0,root2=0;
				long[] arr=new long[(int) n];
				for(int i=0;i<n;i++){
					arr[i]=scn.nextLong();
					root1=Math.sqrt(arr[i]);
					root2=(int)(Math.sqrt(arr[i]));
					if(arr[i]==1){
						p.println("NO");
					}
					else if(root1==root2){
						if(pre[(int) root1]){
						p.println("YES");
						}
						else{
						p.println("NO");
						}
					}
					else{
						p.println("NO");
					}
				}
				p.close();
				
			}
	}