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.*;
import java.util.*;

public class B {
  public static void main(String[] args) throws IOException {
    BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
    int n = Integer.parseInt(f.readLine());
    StringTokenizer st = new StringTokenizer(f.readLine());
    HashSet<Long> set = primeSquares();
    while (n-- > 0) 
      System.out.println(set.contains(Long.parseLong(st.nextToken()))
          ? "YES" : "NO");
  }

  public static HashSet<Long> primeSquares() {
    int sqrtLim = 1000001;
    boolean[] arr = new boolean [sqrtLim];
    for (int i = 2; i*i < sqrtLim; i++) 
      if (!arr[i]) 
        for (int j = i * i; j < sqrtLim; j+=i)
          arr[j] = true;
    HashSet<Long> res = new HashSet<Long>();
    for (int i = 2; i < sqrtLim; i++)
      if (!arr[i]) {
        res.add((long) i * i);
      }
    return res;
  }
}