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.BufferedReader;
import java.io.DataInputStream;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.StringTokenizer;
 
public class Main{
 
    static class InputReader {
 
        final private int BUFFER_SIZE = 1 << 17;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public InputReader(InputStream in) {
            din = new DataInputStream(in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public byte next() {
            try {
                return read();
            } catch (Exception e) {
                throw new InputMismatchException();
            }
        }
 
        public String nextString() {
            StringBuilder sb = new StringBuilder("");
            byte c = next();
            while (c <= ' ') {
                c = next();
            }
            do {
                sb.append((char) c);
                c = next();
            } while (c > ' ');
            return sb.toString();
        }
 
        public int nextInt() {
            int ret = 0;
            byte c = next();
            while (c <= ' ') {
                c = next();
            }
            boolean neg = c == '-';
            if (neg) {
                c = next();
            }
            do {
                ret = (ret << 3) + (ret << 1) + c - '0';
                c = next();
            } while (c > ' ');
            if (neg) {
                return -ret;
            }
            return ret;
        }
 
        private void fillBuffer() {
            try {
                bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (bytesRead == -1) {
                buffer[0] = -1;
            }
        }
 
        private byte read() {
            if (bufferPointer == bytesRead) {
                fillBuffer();
            }
            return buffer[bufferPointer++];
        }
    }
   
    public static void main(String arg[]) throws IOException {
   
       // InputReader r=new InputReader(System.in);
      //  BufferedReader r=new BufferedReader(new FileReader("testcase.txt"));
        BufferedReader r=new BufferedReader(new InputStreamReader(System.in));
boolean prime[]=new boolean[1000001];
Arrays.fill(prime, true);

for(int i=2;i*i<=1000000;i++)
{
    if(prime[i])
    {
        for(int j=2;j*i<=1000000;j++)
            prime[i*j]=false;
    }
}
prime[1]=false;
        int n=Integer.parseInt(r.readLine());
         StringTokenizer str=new StringTokenizer(r.readLine());
for(int i=1;i<=n;i++)
        {
        long x=Long.parseLong(str.nextToken());
        
        double d=Math.sqrt(x);
        if(d==Math.round(d)&&prime[(int)d])
        {
            System.out.println("YES");
        }
        else
            System.out.println("NO");
        }
    }}