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.BufferedWriter;
import java.io.Closeable;
import java.io.Flushable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class TPrimes {

    static Reader in = new Reader(System.in);
    static Writer out = new Writer(System.out);

    public static void main(String[] args) throws IOException {

        int n = in.nextInt();
        long x;
        double s;
        while (n-- > 0) {
            x = in.nextLong();
            s = Math.sqrt(x);
            out.println(s % 1 == 0 && isPrime((long) s) ? "YES" : "NO");

        }
        in.close();
        out.flush();
        out.close();
    }

    public static boolean isPrime(long n) {
        if (n <= 1) {
            return false;
        }
        if (n <= 3) {
            return true;
        }
        if (n % 2 == 0 || n % 3 == 0) {
            return false;
        }

        for (int i = 5; i * i <= n; i = i + 6) {
            if (n % i == 0 || n % (i + 2) == 0) {
                return false;
            }
        }

        return true;
    }

    ////////////////////////////////////////////////////////////////////////////
    /////////////////////////////  INPUT / OUTPUT  /////////////////////////////
    ////////////////////////////////////////////////////////////////////////////
    static class Reader implements Closeable {

        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public Reader(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        private StringTokenizer getTokenizer() throws IOException {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = nextLine();
                if (line == null) {
                    return null;
                }
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer;
        }

        public boolean hasNext() throws IOException {
            return getTokenizer() != null;
        }

        public String next() throws IOException {
            return hasNext() ? tokenizer.nextToken() : null;
        }

        public String nextLine() throws IOException {
            tokenizer = null;
            return reader.readLine();
        }

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

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

        public float nextFloat() throws IOException {
            return Float.parseFloat(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public String[] nextStringArray(int size) throws IOException {
            String[] array = new String[size];
            for (int i = 0; i < size; i++) {
                array[i] = next();
            }
            return array;
        }

        public int[] nextIntArray(int size) throws IOException {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        public long[] nextLongArray(int size) throws IOException {
            long[] array = new long[size];
            for (int i = 0; i < size; i++) {
                array[i] = nextLong();
            }
            return array;
        }

        public double[] nextDoubleArray(int size) throws IOException {
            double[] array = new double[size];
            for (int i = 0; i < size; i++) {
                array[i] = nextDouble();
            }
            return array;
        }

        @Override
        public void close() throws IOException {
            tokenizer = null;
            reader.close();
        }
    }

    static class Writer implements Closeable, Flushable {

        private final PrintWriter writer;

        public Writer(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        @Override
        public void close() {
            writer.close();
        }

        @Override
        public void flush() {
            writer.flush();
        }
    }
}