M × N Puzzle

Time Limit: 4000MS

Memory Limit: 131072K

Description

The Eight Puzzle, among other sliding-tile puzzles, is one of the famous problems in artificial intelligence. Along with chess, tic-tac-toe and backgammon, it has been used to study search algorithms.The Eight Puzzle can be generalized into an M × N Puzzle where at least one of M and N is odd. The puzzle is constructed with MN − 1 sliding tiles with each a number from 1 to MN − 1 on it packed into a M by N frame with one tile missing. For example, with M = 4 and N = 3, a puzzle may look like:
162
403
759
10811

Input

The input consists of multiple test cases. Each test case starts with a line containing M and N (2 M, N ≤ 999). This line is followed by M lines containing N numbers each describing an M × N puzzle.The input ends with a pair of zeroes which should not be processed.

Output

Output one line for each test case containing a single word YES if the puzzle can be solved and NO otherwise.

Sample Input

3 3
1 0 3
4 2 5
7 8 6
4 3
1 2 5
4 6 9
11 8 10
3 7 0
0 0

Sample Output

YES
NO

Hint

Source

POJ Monthly--2006.07.30, newton88518

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