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.util.*;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
 
public class Main {
    public static double PI = Math.acos(-1.0);
    public static double eps = 1e-6;	
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String next() {
            while(tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
    }
    public static int maxn = (int) (1e6 + 5);
    public static boolean[] np = new boolean[maxn];
    public static int[] p = new int[maxn];
    public static int tot;
    public static void init() {
        tot = 0;
        for(int i = 0; i < maxn; ++i) np[i] = false;
        for(int i = 2; i < maxn; ++i) {
            if(np[i] == false) p[tot++] = i;
            for(int j = 0; j < tot; ++j) {
                int num = i*p[j];
                if(num >= maxn) break;
                np[num] = true;
                if(i%p[j] == 0) break;
            }
        }
    }
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        InputReader in = new InputReader(inputStream);
        init();
        int T = in.nextInt();
        for(int cs = 1; cs <= T; ++cs) {
            long x = in.nextLong();
            int sx = (int)Math.sqrt(x);
            if(x == 1 || np[sx] == true || (long)sx*sx != x) System.out.println("NO");
            else System.out.println("YES");
        }
        // Scanner in = new Scanner(System.in);
        // in.close();
    }
}