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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    public static void main(String[] args) throws IOException {
        InputStream stdin = System.in;
        OutputStream stdout = System.out;

        /*
         * InputStream fileIn = new FileInputStream(new File("input.txt"));
         * OutputStream fileOut = new FileOutputStream(new File("output.txt"));
         */

        InputReader in = new InputReader(stdin);
        OutputWriter out = new OutputWriter(stdout);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
}

class Task {
    
    public void solve(InputReader in, OutputWriter out) {
        
        
        int n = in.readInt();
        boolean[]prime = getResheto(1000000);
        for (int i = 0; i < n; i++) {
            long value = in.readLong();
            long sq = (long) Math.sqrt(value);
            if (sq * sq == value) {
                if (prime[(int)sq]) {
                    out.printLine("YES");
                }
                else {
                    out.printLine("NO");
                }
            }
            else {
                out.printLine("NO");
            }
        }
    }
    
    public boolean[] getResheto(int n) {
        boolean[]prime = new boolean[n + 1];
        Arrays.fill(prime, true);
        prime[0] = prime[1] = false;
        for (int i=2; i<=n; ++i)
            if (prime[i])
                if (i * 1L * i <= n)
                    for (int j=i*i; j<=n; j+=i)
                        prime[j] = false;
        return prime;
    }
    
    public void test() {
        for (int i = 0; i < 1000; i++) {
            int count = 0;
            for (int j = 1; j <= i; j++) {
                if (i % j == 0) count++;
            }
            if (count == 3)
            System.out.println(i + " = " + count);
        }
    }
}


class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long readLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public char readCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    public static boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(outputStream);
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

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

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

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