Problem: Little Petya loves playing with squares. Mum bought him a square 2n × 2n in size. Petya marked a cell inside the square and now he is solving the following task.

The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.

Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.

Input

The first line contains three space-separated integers 2n, x and y (2 ≤ 2n ≤ 100, 1 ≤ x, y ≤ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.

The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.

Output

If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).

Examples

Input

4 1 1


Output

YES


Input

2 2 2


Output

NO

Note

A sample test from the statement and one of the possible ways of cutting the square are shown in the picture: 

<image>

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;



public class C85P2 {

    private static BufferedReader in;
    private static PrintWriter out;
    private static StringTokenizer input;
    
    public static void main(String[] args) throws IOException {
        //-------------------------------------------------------------------------
        //Initializing...
        new C85P2();
        //-------------------------------------------------------------------------
        //put your code here... :)
        int n2 = nextInt(),x = nextInt(),y=nextInt();
        int n = n2/2;
        if(x == n && y==n)
            writeln("NO");
        else if (x==n && y==n+1)
            writeln("NO");
        else if (x==n+1 && y==n )
            writeln("NO");
        else if (x==n+1 && y==n+1)
            writeln("NO");
        else writeln("YES");
        //-------------------------------------------------------------------------
        //closing up
        end();
        //--------------------------------------------------------------------------

    }
    public C85P2() throws IOException {
        //Input Output for Console to be used for trying the test samples of the problem 
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        //-------------------------------------------------------------------------
        //Initalize Stringtokenizer input
        input = new StringTokenizer(in.readLine());
    }

    private static int nextInt() throws IOException {
        if (!input.hasMoreTokens())input=new StringTokenizer(in.readLine());
        return Integer.parseInt(input.nextToken());
    }
    private static long nextLong() throws IOException {
        if (!input.hasMoreTokens())input=new StringTokenizer(in.readLine());
        return Long.parseLong(input.nextToken());
    }
    private static double nextDouble() throws IOException {
        if (!input.hasMoreTokens())input=new StringTokenizer(in.readLine());
        return Double.parseDouble(input.nextToken());
    }
    private static String nextString() throws IOException {
        if (!input.hasMoreTokens())input=new StringTokenizer(in.readLine());
        return input.nextToken();
    }
    private static void write(String output){
        out.write(output);
        out.flush();
    }
    private static void writeln(String output){
        out.write(output+"\n");
        out.flush();
    }
    private static void end() throws IOException{
        in.close();
        out.close();
        System.exit(0);
    }

    

}