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.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;

/**
 * Works good for CF
 * 
 * @author cykeltillsalu
 */
public class B142 {

	long ps[];
	{
		int num = (int) (Math.sqrt(1000000000000L) + 1);
		boolean[] isPrime = new boolean[num + 1];
		Arrays.fill(isPrime, true);
		isPrime[0] = isPrime[1] == false;
		int cnt = 0;
		for (int i = 2; i <= num; i++) {
			int step = i, tmp = i * 2;
			if (isPrime[i]) {
				cnt++;
				while (tmp <= num) {
					isPrime[tmp] = false;
					tmp += step;
				}
			}
		}
		ps = new long[cnt];
		int pos = 0;
		for (int i = 2; i < isPrime.length; i++) {
			if (isPrime[i]) {
				ps[pos] = i;
				pos++;
			}
		}
	}

	// some local config
	static boolean test = false;
	static String testDataFile = "testdata.txt";
	static String feedFile = "feed.txt";
	CompetitionType type = CompetitionType.CF;
	private static String ENDL = "\n";

	// solution
	private void solve() throws Throwable {

		int n = iread();
		long[] r = new long[n];
		boolean[] cnt = new boolean[n];
		for (int i = 0; i < n; i++) {
			r[i] = lread();
		}
		Set<Long> candidates = new HashSet<Long>();
		for (int i = 0; i < ps.length; i++) {
			candidates.add(ps[i] * ps[i]);
		}

		for (int j = 0; j < r.length; j++) {
			if (candidates.contains(r[j])) {
				cnt[j] = true;
			}
		}

		for (int i = 0; i < n; i++) {
			out.write(cnt[i] ? "YES" : "NO");
			out.write("\n");
		}
		out.flush();
	}

	public static boolean isPrime(long n) {
		boolean prime = true;
		for (long i = 3; i <= Math.sqrt(n); i += 2)
			if (n % i == 0) {
				prime = false;
				break;
			}
		if ((n % 2 != 0 && prime && n > 2) || n == 2) {
			return true;
		} else {
			return false;
		}
	}

	public int iread() throws Exception {
		return Integer.parseInt(wread());
	}

	public double dread() throws Exception {
		return Double.parseDouble(wread());
	}

	public long lread() throws Exception {
		return Long.parseLong(wread());
	}

	public String wread() throws IOException {
		StringBuilder b = new StringBuilder();
		int c;
		c = in.read();
		while (c >= 0 && c <= ' ')
			c = in.read();
		if (c < 0)
			return "";
		while (c > ' ') {
			b.append((char) c);
			c = in.read();
		}
		return b.toString();
	}

	public static void main(String[] args) throws Throwable {

		if (test) { // run all cases from testfile:
			BufferedReader testdataReader = new BufferedReader(new FileReader(testDataFile));
			String readLine = testdataReader.readLine();
			int casenr = 0;
			out: while (true) {
				BufferedWriter w = new BufferedWriter(new FileWriter(feedFile));
				if (!readLine.equalsIgnoreCase("input")) {
					break;
				}
				while (true) {
					readLine = testdataReader.readLine();
					if (readLine.equalsIgnoreCase("output")) {
						break;
					}
					w.write(readLine + "\n");
				}
				w.close();
				System.out.println("Answer on case " + (++casenr) + ": ");

				new B142().solve();
				System.out.println("Expected answer: ");

				while (true) {
					readLine = testdataReader.readLine();

					if (readLine == null) {
						break out;
					}
					if (readLine.equalsIgnoreCase("input")) {
						break;
					}
					System.out.println(readLine);
				}
				System.out.println("----------------");
			}
			testdataReader.close();
		} else { // run on server
			new B142().solve();
		}
		out.close();
	}

	public B142() throws Throwable {
		if (test) {
			in = new BufferedReader(new FileReader(new File(feedFile)));
		}
	}

	InputStreamReader inp = new InputStreamReader(System.in);
	BufferedReader in = new BufferedReader(inp);
	static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

	enum CompetitionType {
		CF, OTHER
	};
}