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 Main {


    public static void main(String [] args){
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Integer readFromFile=new Integer(1);
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }
    static class TaskD {

        final int maxValue = 1000_001;
        byte [] prime = new byte[maxValue];
        void eratos(){
            prime[1] = 1;
            for(int i=2; i*i<maxValue; i++){
                if(prime[i]==0){
                    for(int j=i*i; j<maxValue;j+=i){
                        prime[j]=1;
                    }
                }
            }
        }
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            eratos();
            int n = in.nextInt();
            line1: for(int i=0; i<n; i++){
                long x = in.nextLong();
                for(long l=1, r=maxValue; l<=r; ){
                    long c = (l+r)/2;
                    if(c*c==x){
                        if(prime[(int)c]==0) {
                            out.println("YES");
                        }else{
                            out.println("NO");
                        }
                        continue line1;
                    }else if(c*c<x){
                        l = c+1;
                    }else{
                        r = c-1;
                    }
                }
                out.println("NO");
            }
        }
    }
    class Pair{
        int first;
        int second;
        Pair(int first, int second){
            this.first = first;
            this.second = second;
        }
    }
    void madAdd(Map <Character, Integer> map, char value){
        if(map.containsKey(value)){
            map.put(value, map.get(value)+1);
        }else{
            map.put(value, 1);
        }
    }
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;
        String st1;
        File file = new File("text.txt");
        public InputReader(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }
        public InputReader(int i) {
            try {
                br  = new BufferedReader(
                        new InputStreamReader(new FileInputStream(file)));
            } catch (FileNotFoundException e1) {
                System.out.println("File is not find");
            }
            st = null;
        }
        public String next(){
            while (st==null || !st.hasMoreTokens()){
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }
        public String nextLine(){
            try {
                st1 = new String(br.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return st1;
        }
        public int nextInt()  {return Integer.parseInt(next());}
        public long nextLong(){
            return Long.parseLong(next());
        }
        public Double nextDouble(){
            return Double.parseDouble(next());
        }
        public Byte nextByte() {
            return Byte.parseByte(next());
        }
        private int idx;
        public Character nextChar() {
            if(st1==null) {
                st1 = next();
                idx = 0;
            }
            if(idx!=(st1.length())-1){
                return st1.charAt(idx++);
            }else{
                char  c= st1.charAt(idx);
                st1 = null;
                return c;
            }
        }
        public void newFile() {
            try {
                FileWriter write = new FileWriter(file);
                write.write("something for cheaking");
                write.close();

            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        public void writeFile1(){
            try{
                FileWriter write = new FileWriter(file);
                write.append("100000"+" ");
                for(int i=0; i<100000; i++){
                    write.append(new Integer((int)(Math.random()*5000)).toString()+" ");
                }
                write.close();

            }catch(IOException e){
                e.printStackTrace();
            }
        }
    }
}