Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Petya and Square

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLittle Petya loves playing with squares. Mum bought him a square 2*n* × 2*n* 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 2*n*, *x* and *y* (2 ≤ 2*n* ≤ 100, 1 ≤ *x*, *y* ≤ 2*n*), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2*n* 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 2*n*. 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:

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/25/2018 20:14:03 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|