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 AiseHi {
	static class FastReader
	{
	BufferedReader br;
	StringTokenizer st;

	public FastReader()
	{
	br = new BufferedReader(new
	InputStreamReader(System.in));
	}

	String next()
	{
	while (st == null || !st.hasMoreElements())
	{
	try
	{
	st = new StringTokenizer(br.readLine());
	}
	catch (IOException e)
	{
	e.printStackTrace();
	}
	}
	return st.nextToken();
	}

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

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

	double nextDouble()
	{
	return Double.parseDouble(next());
	}

	String nextLine()
	{
	String str = "";
	try
	{
	str = br.readLine();
	}
	catch (IOException e)
	{
	e.printStackTrace();
	}
	return str;
	}
	}
	static int m = (int)(1e9+9);
	static long mod(long x) {
		return ((x%m + m)%m);
	}
	static long add(long a,long b) {
		return mod(mod(a)+mod(b));
	}
	static long mul(long a,long b) {
		return mod(mod(a) * mod(b));
	}
	
	public static void main (String[] args) {
		FastReader sc = new FastReader();
		int n = sc.nextInt();
		long a[] = new long[n];
		for(int i=0;i<n;i++) a[i] = sc.nextLong();
		sieve();
		for(int i=0;i<n;i++) {
			long x = a[i];
			long sq = sqrt(x);
			if(sq!=-1 && !prime[(int)sq]) System.out.println("YES"); 
			else System.out.println("NO");
		}
	}
	private static long sqrt(long x) {
		long l = 1,h = x;
		long ans = 0;
		while(l<=h) {
			long mid = (l+(h-l)/2);
			if(mid>x/mid) h = mid-1;
			else {
				ans = mid;
				l = mid+1;
			}
		}
		if(ans*ans==x) return ans;
		else return -1;
	}
	static boolean prime[] = new boolean[10000001];
	static void sieve() {
		prime[0] = true;
		prime[1] = true;
		int max = 10000000;
		for(int i=2;i*i<=max;i++) {
			if(!prime[i]) {
				for(int j=i*i;j<=max;j+=i)
					prime[j] = true;
			}
		}
	}
	static String reverse(String x) {
		StringBuilder input1 = new StringBuilder();
		
        input1.append(x);
        
        input1 = input1.reverse();
        
        return input1.toString();
	}
	static int gcd(int val, int g) {
		if(g==0) return val;
		
		return gcd(g,val%g);
	}
}