CF191C Fools and Roads

They say that Berland has exactly two problems, fools and roads. Besides, Berland has $ n $ cities, populated by the fools and connected by the roads. All Berland roads are bidirectional. As there are many fools in Berland, between each pair of cities there is a path (or else the fools would get upset). Also, between each pair of cities there is no more than one simple path (or else the fools would get lost). But that is not the end of Berland's special features. In this country fools sometimes visit each other and thus spoil the roads. The fools aren't very smart, so they always use only the simple paths. A simple path is the path which goes through every Berland city not more than once. The Berland government knows the paths which the fools use. Help the government count for each road, how many distinct fools can go on it. Note how the fools' paths are given in the input.

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In the first sample the fool number one goes on the first and third road and the fool number 3 goes on the second, first and fourth ones. In the second sample, the fools number 1, 3 and 5 go on the first road, the fool number 5 will go on the second road, on the third road goes the fool number 3, and on the fourth one goes fool number 1.