Vasya is very fond of various games: checkers, chess, dominoes, tic-tac-toe, etc. Since he has been playing them for quite a long time, he managed to learn these games quite well, and they became boring. Therefore, he now invents new games based on those he has already played enough. He recently invented the game Domino Chess.
It consists of the following: Vasya takes a large piece of plywood from his grandfather and paints it in such a way that he gets a chessboard of size N × M cells. Then he takes domino bones and tries to cover the resulting board with them so that all the cells are closed, there are no overlaps and no dominoes stick out over the edges of the board (each domino covers two adjacent cells).
Since Vasya does not ask grandfather's permission before taking a board, he sometimes takes boards that are not needed, and sometimes those that grandfather wanted to use in the construction of a new dacha. Just today, Vasya took the "necessary" board, so grandfather was forced to cut two squares of one cell from Vasya's board.
At first, Vasya was upset that he would not be able to play his game. And then I decided to try to pave the board with the cells already cut out, and in such a way that the cut cells were not covered with dominoes.
Help Vasya understand if this can be done.
Input
The first line of the input contains numbers N and M — board dimensions (1 ≤ N ≤ 200, 1 ≤ M ≤ 200, N·M > 2).
The second line contains two space-separated integers — x1 and y1 coordinates of the first cut cell (1 ≤ x1 ≤ N, 1 ≤ y1 ≤ M).
The third line contains two space-separated integers — x2 and y2 coordinates of the second cut cell (1 ≤ x2 ≤ N, 1 ≤ y2 ≤ M).
The first and second cells do not match.
Imprint
Print "YES" if the board with cut out cells can be covered with dominoes, and "NO" otherwise. (Vasya's supply of dominoes is endless.)
Examples
| # |
Input |
Output |
| 1 |
2 2
1 1
2 2 |
NO |
| 2 |
2 2
1 1
1 2
| YES |