CF167E Wizards and Bets

In some country live wizards. They like to make weird bets. Two wizards draw an acyclic directed graph with $ n $ vertices and $ m $ edges (the graph's vertices are numbered from $ 1 $ to $ n $ ). A source is a vertex with no incoming edges, and a sink is the vertex with no outgoing edges. Note that a vertex could be the sink and the source simultaneously. In the wizards' graph the number of the sinks and the sources is the same. Wizards numbered the sources in the order of increasing numbers of the vertices from $ 1 $ to $ k $ . The sinks are numbered from $ 1 $ to $ k $ in the similar way. To make a bet, they, as are real wizards, cast a spell, which selects a set of $ k $ paths from all sources to the sinks in such a way that no two paths intersect at the vertices. In this case, each sink has exactly one path going to it from exactly one source. Let's suppose that the $ i $ -th sink has a path going to it from the $ a_{i} $ 's source. Then let's call pair $ (i,j) $ an inversion if $ i<j $ and $ a_{i}>a_{j} $ . If the number of inversions among all possible pairs $ (i,j) $ , such that $ (1

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In the first sample, there is exactly one set of paths — . The number of inversions is 0, which is an even number. Therefore, the first wizard gets 1 coin. In the second sample there is exactly one set of paths — . There is exactly one inversion. Therefore, the first wizard gets -1 coin. . In the third sample, there are two sets of paths, which are counted with opposite signs. In the fourth sample there are no set of paths at all. In the fifth sample, there are three sources — the vertices with the numbers (2, 3, 5) and three sinks — the vertices with numbers (1, 2, 4). For a single set of paths  are 2 inversions, that is, their number is even.