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.math.*;
import java.io.*;

public class Solution {
    

    static Random random = new Random();

    public static void main(String[] args) throws IOException{
        
        FastScanner scanner = new FastScanner(System.in);
        
        boolean[] arr = new boolean[1000001];
        for(int i = 2; i * i <= 1000000; i++) {
            if(!arr[i]) {
                for(int j = i + i; j <= 1000000; j += i) {
                    arr[j] = true;
                }
            }
        }
        
        int n = scanner.nextInt();
        for(int i = 0; i < n; i++) {
            long x = scanner.nextLong();
            double sqrt = Math.sqrt(x);
            if((int)sqrt == sqrt && !arr[(int)sqrt] && x != 1) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }
        }

    }

    static void insertionSort(byte[] arr) {
        for(byte i = 1; i < arr.length; i++) {
            byte value = arr[i];
            byte j = i;
            
            while(j > 0 && value < arr[j-1]) {
                arr[j] = arr[j-1];
                --j;
            }

            if(i != j) {
                arr[j] = value;
            }
        }
    }

    static void swap(byte[] arr, byte i, byte j) {
        byte temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    static void printArr(byte[] arr) {
        for(byte k: arr) {
            System.out.print(k + ", ");
        }
        System.out.println();
    }


    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch(Exception e) {
                e.printStackTrace();
            }
        }

        boolean hasNextToken() {
            if(st == null) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch(IOException e) {
                    
                }
            }
            return st.hasMoreTokens();
        } 

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

            return st.nextToken();
        }

        String nextLine() throws IOException{
            return br.readLine();
        }

        byte nextByte() {
            return Byte.parseByte(next());
        }

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

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

    }

}