CF1131D Gourmet choice

Mr. Apple, a gourmet, works as editor-in-chief of a gastronomic periodical. He travels around the world, tasting new delights of famous chefs from the most fashionable restaurants. Mr. Apple has his own signature method of review — in each restaurant Mr. Apple orders two sets of dishes on two different days. All the dishes are different, because Mr. Apple doesn't like to eat the same food. For each pair of dishes from different days he remembers exactly which was better, or that they were of the same quality. After this the gourmet evaluates each dish with a positive integer. Once, during a revision of a restaurant of Celtic medieval cuisine named «Poisson», that serves chestnut soup with fir, warm soda bread, spicy lemon pie and other folk food, Mr. Apple was very pleasantly surprised the gourmet with its variety of menu, and hence ordered too much. Now he's confused about evaluating dishes. The gourmet tasted a set of $ n $ dishes on the first day and a set of $ m $ dishes on the second day. He made a table $ a $ of size $ n \times m $ , in which he described his impressions. If, according to the expert, dish $ i $ from the first set was better than dish $ j $ from the second set, then $ a_{ij} $ is equal to ">", in the opposite case $ a_{ij} $ is equal to "

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In the first sample, all dishes of the first day are better than dishes of the second day. So, the highest score will be $ 2 $ , for all dishes of the first day. In the third sample, the table is contradictory — there is no possible evaluation of the dishes that satisfies it.