CF475B Strongly Connected City

Imagine a city with $ n $ horizontal streets crossing $ m $ vertical streets, forming an $ (n-1)×(m-1) $ grid. In order to increase the traffic flow, mayor of the city has decided to make each street one way. This means in each horizontal street, the traffic moves only from west to east or only from east to west. Also, traffic moves only from north to south or only from south to north in each vertical street. It is possible to enter a horizontal street from a vertical street, or vice versa, at their intersection. The mayor has received some street direction patterns. Your task is to check whether it is possible to reach any junction from any other junction in the proposed street direction pattern.

The first line of input contains two integers $ n $ and $ m $ , ( $ 2

If the given pattern meets the mayor's criteria, print a single line containing "YES", otherwise print a single line containing "NO".

The figure above shows street directions in the second sample test case.