CF1268D Invertation in Tournament

You are given a tournament — complete directed graph. In one operation you can pick any vertex $ v $ and change the direction of all edges with $ v $ on one of the ends (i.e all edges $ u \to v $ change their orientation to $ v \to u $ and vice versa). You want to make the tournament strongly connected with the smallest possible number of such operations if it is possible. Also, if it is possible, you need to find the number of ways to make this number of operations to make graph strongly connected (two ways are different if for some $ i $ vertex that we chose on $ i $ -th operation in one way is different from vertex that we chose on $ i $ -th operation in another way). You only need to find this value modulo $ 998\,244\,353 $ .

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