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.awt.Checkbox;
import java.io.BufferedInputStream;
import java.util.Collections.*;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Queue;
import java.util.Scanner;
import java.util.TreeMap;
import java.math.*;
import java.util.*;
import java.net.*;
import java.nio.IntBuffer;
public class Main {
	public static boolean check(Long t){
		if (t==1) return false;
		long temp=(long) Math.sqrt(t);
		if (temp*temp!=t) return false;
		if (t==4) return true;
		if (temp*temp==t) {
			if (temp%2==0) return false;
			for (int i=3;i<=Math.sqrt(temp);i+=2)
				if (temp%i==0) return false;
			return true;
		}
		return false;
	}
	public static void main(String[]args) throws NumberFormatException, IOException{
		BufferedReader bufferedReader=new BufferedReader(new InputStreamReader(System.in));
		HashMap<Long, Boolean>t1=new HashMap<>();
		int n=Integer.parseInt(bufferedReader.readLine());
		StringTokenizer stringTokenizer=new StringTokenizer(bufferedReader.readLine());
		for (int i=0;i<n;i++){
			boolean flag=false;
			long temp=Long.parseLong(stringTokenizer.nextToken());
			if (t1.get(temp)!=null){
				flag=t1.get(temp);
			}
			else{
			flag=check(temp);
			t1.put(temp, flag);
			}
			if (flag) System.out.println("YES");
			else System.out.println("NO");
		}
		
	}
}