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.*;
import java.util.*;

public class Tester2 {

	public static void main(String[] args) {
		
		InputReader sc = new InputReader(System.in);
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		int n = 1000000;
		int q  = sc.nextInt();
        // initially assume all integers are prime
        boolean[] isPrime = new boolean[n+1];
        for (int i = 2; i <= n; i++) {
            isPrime[i] = true;
        }

        // mark non-primes <= n using Sieve of Eratosthenes
        for (int factor = 2; factor*factor <= n; factor++) {

            // if factor is prime, then mark multiples of factor as non prime
            // suffices to consider multiples factor, factor+1, ...,  n/factor
            if (isPrime[factor]) {
                for (int j = factor; factor*j <= n; j++) {
                    isPrime[factor*j] = false;
                }
            }
        }
        for(int i=0;i<q;i++)
        {
        	long t = sc.nextLong();
        	long x = (long) Math.sqrt(t);
        	if((x*x) == t)
        	{
        		if(isPrime[(int)x]==true)
        		out.println("YES");
        		else
        			out.println("NO");
        	}
        	else
        		out.println("NO");
        }

		out.close();	
	}
		
		
		static long modulo(long a,long b,long c) {
			long x=1;
			long y=a;
			while(b > 0){
				if(b%2 == 1){
					x=(x*y)%c;
				}
				y = (y*y)%c; // squaring the base
				b /= 2;
			}
			return  x%c;
		}
	}
		

		class InputReader { 
			public BufferedReader reader;
			public StringTokenizer tokenizer;
	 
			public InputReader(InputStream inputstream) {
				reader = new BufferedReader(new InputStreamReader(inputstream));
				tokenizer = null;
			}
	 
			public String nextLine(){
				String fullLine=null;
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					try {
						fullLine=reader.readLine();
					} catch (IOException e) {
						throw new RuntimeException(e);
					}
					return fullLine;
				}
				return fullLine;
			}
			public String next() {
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					try {
						tokenizer = new StringTokenizer(reader.readLine());
					} catch (IOException e) {
						throw new RuntimeException(e);
					}
				}
				return tokenizer.nextToken();
			}
			public long nextLong() {
				return Long.parseLong(next());
			}
			public int nextInt() {
				return Integer.parseInt(next());
			}
			public double nextDouble() {
		          return Double.parseDouble(next());
		      }
		}