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

public class TPrimes {
    public static void main(String[] args) {
    InputReader in = new InputReader(System.in);
    OutputWriter out = new OutputWriter(System.out);
    int n = in.readInt();
    boolean arr[] = primes(1000000);
    for (int i = 0; i < n; i++) {
        long x = in.readLong();
        long num = (long) Math.sqrt(x);
        long perfect = num * num;
        if (perfect == x && !arr[(int) num])
        out.printLine("YES");
        else
        out.printLine("NO");
    }
    out.close();
    }

    private static boolean[] primes(int n) {
    boolean[] arr = new boolean[n + 1];
    arr[0] = true;
    arr[1] = true;
    for (int i = 2; i <= Math.sqrt(n); i++)
        if (!arr[i])
        for (int k = i * i; k <= n; k = k + i)
            arr[k] = true;
    return arr;
    }

    static 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 String readLine() {
        int c = read();
        while (isSpaceChar(c))
        c = read();
        StringBuilder res = new StringBuilder();
        do {
        res.appendCodePoint(c);
        c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    }

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

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

    public boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }
    }

    static class OutputWriter {
    private final PrintWriter writer;

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