CF173D Deputies

The Trinitarian kingdom has exactly $ n=3k $ cities. All of them are located on the shores of river Trissisipi, which flows through the whole kingdom. Some of the cities are located on one side of the river, and all the rest are on the other side. Some cities are connected by bridges built between them. Each bridge connects two cities that are located on the opposite sides of the river. Between any two cities exists no more than one bridge. The recently inaugurated King Tristan the Third is busy distributing his deputies among cities. In total there are $ k $ deputies and the king wants to commission each of them to control exactly three cities. However, no deputy can be entrusted to manage the cities, which are connected by a bridge — the deputy can set a too high fee for travelling over the bridge to benefit his pocket, which is bad for the reputation of the king. Help King Tristan the Third distribute the deputies between the cities, if it is possible.

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