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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Vector;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Mohamed Hashem
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        int[] sieve = new int[(int) 1e6 + 1];
        Vector<Long> ans = new Vector<>();

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            generate();
            Primes();
            int n = in.nextInt();
            for (int i = 0; i < n; ++i) {
                long m = in.nextLong();
                int st = 0;
                int en = ans.size() - 1;
                boolean c = false;
                while (st <= en) {
                    int mid = (st + en) / 2;
                    if (ans.elementAt(mid) == m) {
                        c = true;
                        break;
                    } else if (ans.elementAt(mid) < m) {
                        st = mid + 1;
                    } else if (ans.elementAt(mid) > m) {
                        en = mid - 1;
                    }
                }
                if (c == true) {
                    out.println("YES");
                } else out.println("NO");
            }
        }

        void generate() {
            for (int i = 0; i <= (int) 1e6; ++i)
                sieve[i] = 1;
            sieve[0] = sieve[1] = 0;
            for (int i = 2; i <= (int) 1e6; ++i) {
                if (sieve[i] == 0) continue;
                else {
                    for (long j = (long) i * i; j <= (int) 1e6; j += i) {
                        sieve[(int) j] = 0;
                    }
                }
            }
        }

        void Primes() {
            for (long i = 2; i <= (int) 1e6; ++i) {
                if (sieve[(int) i] == 1) {
                    ans.add((i * i));
                }
            }
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

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

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

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

    }
}