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.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public final class Main{
	public static void main(String[] args)throws Exception{
		new Main().solve();
	}
	public static void solve()throws Exception{//last in pg28...
		String[] s;
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		s = br.readLine().split(" ");
		br.close();
		boolean[] primes = new boolean[1000000+1];
		Arrays.fill(primes,true);
		for(long p=2;p*p<=primes.length-1;p++){
			if(primes[(int)p]==true){
				for(long i=p*2;i<=primes.length-1;i+=p){
					primes[(int)i]=false;
				}
			}
		}
		HashSet<Long> set = new HashSet<Long>();
		for(long i=2;i<primes.length;i++){
			if(primes[(int)i]==true){
				set.add(new Long(i*i));
			}
		}
		for(int i=0;i<n;i++){
			long num = Long.parseLong(s[i]);
			if(set.contains(num)){
				System.out.println("YES");
			}else{
				System.out.println("NO");
			}
		}
	}
}