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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;

public class B_Primes {

    static BitSet primes = new BitSet(10000001);
    static ArrayList<Long> tprimes = new ArrayList<Long>();
    static long[] tprime = new long[78498];
    static int counter = 0;

    public static void main(String[] args) throws NumberFormatException,
            IOException {

        Update();
        int n;
        
        BufferedWriter w = new BufferedWriter(
                new OutputStreamWriter(System.out));
        BufferedReader x = new BufferedReader(new InputStreamReader(System.in));
        n = Integer.parseInt(x.readLine().trim());
        String Line = x.readLine();
        String[] temps = Line.split("\\s+");
        for (int i = 0; i < n; i++) {
            long val = Long.parseLong(temps[i]);
            if (Arrays.binarySearch(tprime, val) >= 0) {
                w.append("YES\n");
            } else
                w.append("NO\n");
        }
        w.flush();
        w.close();

    }

    private static void Update() {

        primes.set(2, 1000000);
        tprime[counter++] = 4;
        for (int i = 4; i < 1000001; i += 2) {
            primes.clear(i);
        }

        for (int i = 3; i < 1000001; i++) {
            if (primes.get(i)) {
                tprime[counter++] = new Long(i) * (i);
                int count = 3;
                for (; i * count < 1000001; count += 2)
                    primes.clear(i * count);
            }
        }

    }
}