A Gift From the Stars

A graph with $(k+1)$ vertices and $k$ edges is called a level-$k\ (k\geq 2)$ star if and only if: * it has a vertex that is connected to each of the other $k$ vertices with an edge, and there are no other edges. At first, Takahashi had a graph consisting of stars. He repeated the following operation until every pair of vertices in the graph was connected: * choose two vertices in the graph. Here, the vertices must be disconnected, and their degrees must be both $1$. Add an edge that connects the chosen two vertices. He then arbitrarily assigned an integer from $1$ through $N$ to each of the vertices in the graph after the procedure. The resulting graph is a tree; we call it $T$. $T$ has $(N-1)$ edges, the $i$\-th of which connects $u_i$ and $v_i$. Takahashi has now forgotten the number and levels of the stars that he initially had. Find them, given $T$. ## Constraints * $3\leq N\leq 2\times 10^5$ * $1\leq u_i, v_i\leq N$ * The given graph is an $N$\-vertex tree obtained by the procedure in the problem statement. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $u_1$ $v_1$ $\vdots$ $u_{N-1}$ $v_{N-1}$ [samples]