{"problem":{"name":"Uninity","description":{"content":"We will recursively define _uninity_ of a tree, as follows: (_Uni_ is a Japanese word for sea urchins.) *   A tree consisting of one vertex is a tree of uninity $0$. *   Suppose there are zero or mor","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc009_d"},"statements":[{"statement_type":"Markdown","content":"We will recursively define _uninity_ of a tree, as follows: (_Uni_ is a Japanese word for sea urchins.)\n\n*   A tree consisting of one vertex is a tree of uninity $0$.\n*   Suppose there are zero or more trees of uninity $k$, and a vertex $v$. If a vertex is selected from each tree of uninity $k$ and connected to $v$ with an edge, the resulting tree is a tree of uninity $k+1$.\n\nIt can be shown that a tree of uninity $k$ is also a tree of uninity $k+1,k+2,...$, and so forth.\nYou are given a tree consisting of $N$ vertices. The vertices of the tree are numbered $1$ through $N$, and the $i$\\-th of the $N-1$ edges connects vertices $a_i$ and $b_i$.\nFind the minimum $k$ such that the given tree is a tree of uninity $k$.\n\n## Constraints\n\n*   $2 ≦ N ≦ 10^5$\n*   $1 ≦ a_i, b_i ≦ N(1 ≦ i ≦ N-1)$\n*   The given graph is a tree.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$a_1$ $b_1$\n:\n$a_{N-1}$ $b_{N-1}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc009_d","tags":[],"sample_group":[["7\n1 2\n2 3\n2 4\n4 6\n6 7\n7 5","2\n\nA tree of uninity $1$ consisting of vertices $1$, $2$, $3$ and $4$ can be constructed from the following: a tree of uninity $0$ consisting of vertex $1$, a tree of uninity $0$ consisting of vertex $3$, a tree of uninity $0$ consisting of vertex $4$, and vertex $2$.\nA tree of uninity $1$ consisting of vertices $5$ and $7$ can be constructed from the following: a tree of uninity $1$ consisting of vertex $5$, and vertex $7$.\nA tree of uninity $2$ consisting of vertices $1$, $2$, $3$, $4$, $5$, $6$ and $7$ can be constructed from the following: a tree of uninity $1$ consisting of vertex $1$, $2$, $3$ and $4$, a tree of uninity $1$ consisting of vertex $5$ and $7$, and vertex $6$."],["12\n1 2\n2 3\n2 4\n4 5\n5 6\n6 7\n7 8\n5 9\n9 10\n10 11\n11 12","3"]],"created_at":"2026-03-03 11:01:14"}}