{"raw_statement":[{"iden":"problem statement","content":"Takahashi has decided to make a _Christmas Tree_ for the Christmas party in AtCoder, Inc.\nA Christmas Tree is a tree with $N$ vertices numbered $1$ through $N$ and $N-1$ edges, whose $i$\\-th edge $(1\\leq i\\leq N-1)$ connects Vertex $a_i$ and $b_i$.\nHe would like to make one as follows:\n\n*   Specify two non-negative integers $A$ and $B$.\n*   Prepare $A$ _Christmas Paths_ whose lengths are at most $B$. Here, a Christmas Path of length $X$ is a graph with $X+1$ vertices and $X$ edges such that, if we properly number the vertices $1$ through $X+1$, the $i$\\-th edge $(1\\leq i\\leq X)$ will connect Vertex $i$ and $i+1$.\n*   Repeat the following operation until he has one connected tree:\n    *   Select two vertices $x$ and $y$ that belong to different connected components. Combine $x$ and $y$ into one vertex. More precisely, for each edge $(p,y)$ incident to the vertex $y$, add the edge $(p,x)$. Then, delete the vertex $y$ and all the edges incident to $y$.\n*   Properly number the vertices in the tree.\n\nTakahashi would like to find the lexicographically smallest pair $(A,B)$ such that he can make a Christmas Tree, that is, find the smallest $A$, and find the smallest $B$ under the condition that $A$ is minimized.\nSolve this problem for him."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 10^5$\n*   $1 \\leq a_i,b_i \\leq N$\n*   The given graph is a tree."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $b_1$\n:\n$a_{N-1}$ $b_{N-1}$"},{"iden":"sample input 1","content":"7\n1 2\n2 3\n2 4\n4 5\n4 6\n6 7"},{"iden":"sample output 1","content":"3 2\n\nWe can make a Christmas Tree as shown in the figure below:\n![image](https://img.atcoder.jp/arc088/96f78221624d6a13628f6052f5db697d.png)"},{"iden":"sample input 2","content":"8\n1 2\n2 3\n3 4\n4 5\n5 6\n5 7\n5 8"},{"iden":"sample output 2","content":"2 5"},{"iden":"sample input 3","content":"10\n1 2\n2 3\n3 4\n2 5\n6 5\n6 7\n7 8\n5 9\n10 5"},{"iden":"sample output 3","content":"3 4"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}