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

public class Main {
	public static void main( String[] args ) throws IOException {
		InputStream is = System.in;
		OutputStream os = System.out;
		InputReader inr = new InputReader( is );
		PrintWriter out = new PrintWriter( os );

		Task KillerCage = new Task();
		KillerCage.solve( inr, out );

		out.close();
	}
}



class Task {
	InputReader inr;
	PrintWriter out;

	public void solve( InputReader inr, PrintWriter out ) {
		this.inr = inr; this.out = out;
		int n = inr.nextInt(); n >>= 1;
		int x = inr.nextInt(), y = inr.nextInt();
		boolean flag = true;
		for( int i = n; i <= n + 1; i ++ ) {
			for ( int j = n; j <= n + 1; j ++ ) {
				if ( x == i && y == j ) {
					flag = false;
				}
			}
		}
		if ( flag ) out.printf( "YES" );
		else out.printf( "NO" );
	}
}



class InputReader {
	private InputStream is;
	int cur_byte_idx = 0;
	int bytes_in_buf = 0;
	byte buf[] = new byte[1024 << 4];

	public InputReader( InputStream is ) {
		this.is = is;
	}

	public int readByte() {
		if ( bytes_in_buf == -1 ) throw new InputMismatchException();
		if ( cur_byte_idx >= bytes_in_buf ) {
			cur_byte_idx = 0;
			try {
				bytes_in_buf = is.read( buf );
			} catch ( IOException e ) {
				throw new InputMismatchException();
			}
			if ( bytes_in_buf <= 0 ) return -1;
		}
		return buf[cur_byte_idx ++];
	}

	public boolean isWhitespace( int c ) {
		return !( c >= 33 && c <= 126 );
	}

	public int skip() {
		int b;
		while ( ( b = readByte() ) != -1 && isWhitespace( b ) ) ;
		return b;
	}

	public Byte nextByte() {
		return ( byte ) skip();
	}

	public int nextInt() {
	// public long nextLong() {
		int b;
		while ( ( b = readByte() ) != -1 && 
			!( ( b >= '0' && b <= '9') || b == '-') );
		int symbol = 1;
		if ( b == '-' ) {
			b = readByte();
			symbol = -1;
		}
		int num = 0;
		// when nextLong: long num = 0;
		while ( true ) {
			if ( b >= '0' && b <= '9' ) {
				num = num * 10 + ( b - '0' );
			} else return symbol * num;
			b = readByte();
		}
	}

	public String next() {
	// public String nextLine() {
	int b = skip();
	StringBuilder sb = new StringBuilder();
	while ( !isWhitespace( b ) && true ) { // next
	// while ( !isWhitespace(b) || b == ' ') { // nextLine
		sb.appendCodePoint( b );
		b = readByte();
	}
	return sb.toString();
	}

	// public byte[] next( int n ) {
	public byte[] nextLine( int n ) {
		byte[] by = new byte[n];
		int b = skip(), len= 0;
		while ( len < n && !isWhitespace( b ) ) {// next
		// while ( len < n && ( !isWhitespace( b ) || b == ' ' ) ) {// nextLine
			by[len ++] = ( byte ) b;
			b = readByte();
		}
		if ( n == len ) return by;
		return Arrays.copyOf( by, len );
	}

	// public double nextDouble() {
	//  return Double.parseDouble( next() );
	// }
}