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.BufferedInputStream;
import java.util.*;
import static java.lang.Math.*;

public class C230B {

	public void solve() throws Exception {
		int n = nextInt();
		int max = 1000001;
		boolean[] isPrime = new boolean[max];
		Arrays.fill(isPrime, true);
		HashSet<Long> Tprimes = new HashSet<Long>();
		for (int i = 2; i < max; i++) {
			if (isPrime[i]) {
				Tprimes.add((long) i * i);
				for (int j = i + i; j < max; j += i) {
					isPrime[j] = false;
				}
			}
		}
		while (n-- > 0) {
			long a = nextLong();
			if (Tprimes.contains(a)) {
				println("YES");
			} else {
				println("NO");
			}
		}

	}

	// ------------------------------------------------------

	void debug(Object... os) {
		System.err.println(Arrays.deepToString(os));
	}

	void print(Object... os) {
		if (os != null && os.length > 0)
			System.out.print(os[0].toString());
		for (int i = 1; i < os.length; ++i)
			System.out.print(" " + os[i].toString());
	}

	void println(Object... os) {
		print(os);
		System.out.println();
	}

	BufferedInputStream bis = new BufferedInputStream(System.in);

	String nextWord() throws Exception {
		char c = (char) bis.read();
		while (c <= ' ')
			c = (char) bis.read();
		StringBuilder sb = new StringBuilder();
		while (c > ' ') {
			sb.append(c);
			c = (char) bis.read();
		}
		return new String(sb);
	}

	String nextLine() throws Exception {
		char c = (char) bis.read();
		while (c <= ' ')
			c = (char) bis.read();
		StringBuilder sb = new StringBuilder();
		while (c != '\n' && c != '\r') {
			sb.append(c);
			c = (char) bis.read();
		}
		return new String(sb);
	}

	int nextInt() throws Exception {
		return Integer.parseInt(nextWord());
	}

	long nextLong() throws Exception {
		return Long.parseLong(nextWord());
	}

	public static void main(String[] args) throws Exception {
		new C230B().solve();
	}
}