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 com.sun.org.apache.xpath.internal.functions.FuncFloor;

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

public class A {
    FastScanner in;
    PrintWriter out;
    String fl = "";

    final String END_OF_FILE = "END OF FILE";

    public void solve() throws IOException {
        int n = in.nextInt();
        boolean[] isPrime = new boolean[1000001];
        for(int i = 2;i<isPrime.length;i++)
            isPrime[i] = true;

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

        for(int i = 0;i<n;i++){
            long a = in.nextLong();
            if(Math.sqrt(a) == Math.floor(Math.sqrt(a)) && a % (long)Math.sqrt(a) == 0 && isPrime[(int)Math.sqrt(a)])
                out.println("YES");
            else out.println("NO");
        }
    }

    //region FastScanner
    public void run() {
        try {
            if (fl == "stdin") {
                in = new FastScanner(new File("input.txt"));
                out = new PrintWriter(new File("output.txt"));
            } else if (fl != "") {
                in = new FastScanner(new File(fl + ".in"));
                out = new PrintWriter(new File(fl + ".out"));
            } else {
                in = new FastScanner();
                out = new PrintWriter(new BufferedOutputStream(System.out));
            }

            solve();

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

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                    return END_OF_FILE;
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

    }

    //endregion

    public static void main(String[] arg) {
        new A().run();
    }
}