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.util.*;
import java.io.*;
import java.math.*;

public class Main{
  /*
  .
  .
  .
  .
  .
  .
  .
  some constants
  .
  */
  /*
  .
  .
  .
  if any
  .
  .
  */
  public static void main(String[] args) throws IOException{
		/*
		.
		.
		.
		.
		.
		.
    */
    int n=ni();
    int val=1000000+1;
    int arr[]=new int[val];
    int i,j;
    arr[0]=arr[1]=0;
    for(i=2;i<val;i++){
      arr[i]=1;
    }
    for(i=2;i<=1000;i++){
      for(j=2*i;j<val;j+=i){
        arr[j]=0;
      }
    }
    long b;
    double x;
    for(i=0;i<n;i++){
      b=nl();
      x=Math.sqrt(b);
      if(x==(int)x && arr[(int)x]==1){
        sop("YES");
      }
      else{
        sop("NO");
      }
    }
    /*

		.
		.
		.
		.
		.
		.
		.
		*/
	}
	/*
	temporary functions
	.
	.
	*/
	/*
	fuctions
	.
	.
	.
	.
	.
	.
	.
	.
	.
	.
	.
	.
	.
	.
	.
	.
	.
	abcdefghijklmnopqrstuvwxyz
	.
	.
	.
	.
	.
	.
	*/
	static int modulo(int j,int m){
		if(j<0)
			return m+j;
		  if(j>=m)
			return j-m;

			return j;
	}
	static final int mod=1000000007;
	static final double eps=1e-8;
	static final long inf=100000000000000000L;
	static final boolean debug=true;
	static Reader in=new Reader();
	static StringBuilder ans=new StringBuilder();
	static long powm(long a,long b,long m){
		long an=1;
		long c=a;
		while(b>0){
			if(b%2==1)
				an=(an*c)%m;
			c=(c*c)%m;
			b>>=1;
		}
		return an;
	}
	static Random rn=new Random();
	static void sop(Object a){System.out.println(a);}
	static int ni(){return in.nextInt();}
	static int[] nia(int n){int a[]=new int[n];for(int i=0;i<n;i++)a[i]=ni();return a;}
	static long nl(){return in.nextLong();}
	static long[] nla(int n){long a[]=new long[n];for(int i=0; i<n; i++)a[i]=nl();return a;}
	static String ns(){return in.next();}
	static String[] nsa(int n){String a[]=new String[n];for(int i=0; i<n; i++)a[i]=ns();return a;}
	static double nd(){return in.nextDouble();}
	static double[] nda(int n){double a[]=new double[n];for(int i=0;i<n;i++)a[i]=nd();return a;}
	static class Reader{
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public Reader(){
			reader=new BufferedReader(new InputStreamReader(System.in),32768);
			tokenizer=null;
		}
		public String next(){
			while(tokenizer==null || !tokenizer.hasMoreTokens()){
				try{
					tokenizer=new StringTokenizer(reader.readLine());
				}
				catch(IOException e){
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt(){
			return Integer.parseInt(next());
		}
		public long nextLong(){
			return Long.parseLong(next());
		}
		public double nextDouble(){
			return Double.parseDouble(next());
		}
	}
}