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.util.*;
import java.io.*;

public class Template {
	
	static Scanner sc = new Scanner(System.in);
	

	public static void main(String[] args) {
		int n = sc.nextInt();
		long[] a = new long[n];
		for(int i=0 ; i<n ; i++) {
			a[i] = sc.nextLong();
		}
		boolean primes[] = new boolean[1000001];
		for(int i=2 ; i<primes.length ; i++) {
			primes[i] = true;
		}
		for(int i=2 ; i<=1000 ; i++) {
			if(isPrime(i)) {
				for(int j=2 ; i*j<primes.length ; j++) {
					primes[j*i] = false;
				}
			}
		}
		
		for(long e:a) {
			double sq = Math.sqrt(e);
			if(sq-Math.floor(sq)==0) {
				if(primes[(int) sq]) System.out.println("YES");
				else System.out.println("NO");
			}else System.out.println("NO");
		}
		
	}
	
	
	
	public static int[] readArray(int n) {
		int[] a = new int[n];
		for(int i=0 ; i<n ; i++) {
			a[i] = sc.nextInt();
		} return a;
	}
	
	public static String giveBinary(long n) {
		StringBuffer sb = new StringBuffer();
		for(int i=20 ; i>=0 ; i--) {
			if(n>=Math.pow(2,i)) {
				n-= Math.pow(2, i);
				sb.append("1");
			}else sb.append("0");
		}
		return sb.toString();
	}
	
	public static int gcd(int a , int b) {
		if(a==0) return b;
		else return gcd(b%a,a);
	}
	
	public static boolean isPrime(long n) {
		for(int i=2 ; i*i<=n ; i++) {
			if(n%i==0) return false;
		}
		return true;
	}

}