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.InputStreamReader;
import java.util.*;

public class Main {

    public static Reader reader = new Reader();

    static Map<Long, Boolean> primeList = new HashMap<>();

    public static void main(String[] args) {
        fillPrimes();
        int n = reader.nextInt();
        List<String> ans = new ArrayList<>();
        for(int k = 0; k < n; k++) {
            long x = reader.nextLong();
            if(primeList.containsKey(x)) {
                ans.add("YES");
            } else {
                ans.add("NO");
            }
        }
        for(int i = 0; i < n; i++) {
            System.out.println(ans.get(i));
        }
    }

    static void fillPrimes() {
        List<Long> isPrime = new ArrayList<>();
        for(int i = 0; i < 1000001; i++) {
            isPrime.add(1L);
        }
        isPrime.set(0, 0L);
        isPrime.set(1, 0L);
        for(int i = 2; i < isPrime.size(); i++) {
            if(isPrime.get(i) == 1) {
                primeList.put((long) i * i, true);
                for(int j = i+i; j < isPrime.size(); j+=i) {
                    isPrime.set(j, 0L);
                }
            }
        }
    }

    static class Reader {
        BufferedReader br;
        StringTokenizer st;

        public Reader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        private String next() {
            while(st == null || !st.hasMoreElements()) {
                try{
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}