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.FileReader;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.StringTokenizer;

public class Solution {
    static class Escanner {
        BufferedReader in;
        StringTokenizer st;

        Escanner() throws Throwable {
            in = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer("");
        }

        Escanner(FileReader file) throws Throwable {
            in = new BufferedReader(file);
            st = new StringTokenizer("");
        }

        int nextInt() throws Throwable {
            if (st.hasMoreTokens())
                return Integer.parseInt(st.nextToken());
            st = new StringTokenizer(in.readLine());
            return nextInt();
        }

        long nextLong() throws Throwable {
            if (st.hasMoreTokens())
                return Long.parseLong(st.nextToken());
            st = new StringTokenizer(in.readLine());
            return nextLong();
        }

        BigInteger nextBigInt() throws Throwable {
            if (st.hasMoreTokens())
                return new BigInteger(st.nextToken());
            st = new StringTokenizer(in.readLine());
            return nextBigInt();
        }

        double nextDouble() throws Throwable {
            if (st.hasMoreTokens())
                return Double.parseDouble(st.nextToken());
            st = new StringTokenizer(in.readLine());
            return nextDouble();
        }

        String nextStr() throws Throwable {
            if (st.hasMoreTokens())
                return st.nextToken();
            st = new StringTokenizer(in.readLine());
            return nextStr();
        }
    }
    
    static int n = 1000000;
    static boolean[] isPrime = new boolean[n+1];
    static void seive(){
        isPrime[0] = true;
        isPrime[1] = true;
        for(int i=2; i*i<=n; i++){
            if(!isPrime[i])
                for(int j=i; i*j<=n; j++)
                    isPrime[i*j]=true;
        }
    }
    public static void main(String[] args) throws Throwable {
        Escanner sc = new Escanner();
        int n = sc.nextInt();
        seive();
        for(int i=0; i<n; i++){
            long x = sc.nextLong();
            double y = Math.sqrt(x);
            if(y==(int)y && !isPrime[(int)y])
                System.out.println("YES");
            else
                System.out.println("NO");
        }
    }
}