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.*;
import java.util.*;
import java.math.*;

public class Problem implements Runnable {

        void solve() {
                int n = nextInt();
                int x = nextInt();
                int y = nextInt();
                
                if ((x==n/2 || x==n/2+1) && (y==n/2 || y==n/2+1))
                    out.print("NO");
                else out.print("YES");
        }

        FastScanner sc;
        PrintWriter out;

        public void run() {
                Locale.setDefault(Locale.US);
                try {
                        boolean oj = System.getProperty("ONLINE_JUDGE") != null;
                        if (oj) {
                            sc = new FastScanner(System.in);
                            out = new PrintWriter(System.out);
                        } else {
                            sc = new FastScanner("in.txt");
                            out = new PrintWriter("out.txt");
                        }
                        solve();
                        sc.close();
                        out.close();
                } catch (Throwable e) {
                        e.printStackTrace();
                        System.exit(1);
                }
        }

        int nextInt() {
                return sc.nextInt();
        }

        String nextToken() {
                return sc.nextToken();
        }

        long nextLong() {
                return sc.nextLong();
        }

        double nextDouble() {
                return sc.nextDouble();
        }

        BigInteger nextBigInteger() {
                return sc.nextBigInteger();
        }

        class FastScanner extends BufferedReader {
                StringTokenizer st;
                boolean eof;
                String buf;
                String curLine;
                boolean createST;

                public FastScanner(String fileName) throws FileNotFoundException {
                        this(fileName, true);
                }

                public FastScanner(String fileName, boolean createST)
                                throws FileNotFoundException {
                        super(new FileReader(fileName));
                        this.createST = createST;
                        nextToken();
                }

                public FastScanner(InputStream stream) {
                        this(stream, true);
                }

                public FastScanner(InputStream stream, boolean createST) {
                        super(new InputStreamReader(stream));
                        this.createST = createST;
                        nextToken();
                }

                String nextLine() {
                        String ret = curLine;
                        if (createST) {
                                st = null;
                        }
                        nextToken();
                        return ret;
                }

                String nextToken() {
                        if (!createST) {
                                try {
                                        curLine = readLine();
                                } catch (Exception e) {
                                        eof = true;
                                }
                                return null;
                        }
                        while (st == null || !st.hasMoreTokens()) {
                                try {
                                        curLine = readLine();
                                        st = new StringTokenizer(curLine);
                                } catch (Exception e) {
                                        eof = true;
                                        break;
                                }
                        }
                        String ret = buf;
                        buf = eof ? "-1" : st.nextToken();
                        return ret;
                }

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

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

                double nextDouble() {
                        return Double.parseDouble(nextToken());
                }

                BigInteger nextBigInteger() {
                        return new BigInteger(nextToken());
                }

                public void close() {
                        try {
                                buf = null;
                                st = null;
                                curLine = null;
                                super.close();
                        } catch (Exception e) {

                        }
                }

                boolean isEOF() {
                        return eof;
                }
        }

        public static void main(String[] args) {
                new Problem().run();
        }
}