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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Codeforces {

    static FastScanner sc;
    static PrintWriter out;

    public static void main(String[] args){
        sc = new FastScanner();
        out = new PrintWriter(System.out);

        int t = 1;

        while(t-- > 0){
            solve();
        }

        out.close();
    }

    private static void solve() {

        int n = sc.nextInt();
        long[] arr = new long[n];
        for(int i=0; i<n; i++) {
            arr[i] = sc.nextLong();
        }

        HashSet<Long> tPrimes = new HashSet<>();
        int val = 1000000;
        boolean[] primes = new boolean[val+1];

        primes[0] = true;
        primes[1] = true;

        for(int i=2; i<Math.sqrt(val+1); i++){
            for(int j=i*i; j<val+1; j+=i)
                primes[j] = true;
        }

        for(int i=2; i<= val; i++){
            if(primes[i] == false){
                long temp = (int)i;
                tPrimes.add(temp*temp);
            }
        }

        for(long num: arr){
            if(tPrimes.contains(num))
                out.println("YES");
            else
                out.println("NO");
        }

    }


    private static int findLcm(int n, int m) {

        return n*m/findGcd(Math.min(n, m), Math.max(n, m));
    }

    private static int findGcd(int n, int m) {
        if(n == 0)
            return m;
        return findGcd(m%n, n);
    }

    private static long findLcm(long n, long m) {

        return n*m/findGcd(Math.min(n, m), Math.max(n, m));
    }

    private static long findGcd(long n, long m) {
        if(n == 0)
            return m;
        return findGcd(m%n, n);
    }

    public static void intSort (int[] arr) {
        //First ruffle

        int n = arr.length;
        Random r = new Random();
        for (int i=0; i<arr.length; i++) {
            int j = r.nextInt(n);
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }

        //then sort
        Arrays.sort(arr);
    }

    public static void longSort (long[] arr) {
        //First ruffle

        int n = arr.length;
        Random r = new Random();
        for (int i=0; i<arr.length; i++) {
            int j = r.nextInt(n);
            long temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }

        //then sort
        Arrays.sort(arr);
    }

    public static void sort2dArray (long[][] arr) {
        Arrays.sort(arr, (a, b) -> {
            if (a[1] == b[1])
                return (int) (a[0] - b[0]);
            return (int) (a[1] - b[1]);
        });
    }

    public static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }

}