Uninity

AtCoder

IDagc009_d

Time2000ms

Memory256MB

Difficulty—

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 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 $k+1$. It can be shown that a tree of uninity $k$ is also a tree of uninity $k+1,k+2,...$, and so forth. You 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 $b_i$. Find the minimum $k$ such that the given tree is a tree of uninity $k$. ## Constraints * $2 ≦ N ≦ 10^5$ * $1 ≦ a_i, b_i ≦ N(1 ≦ i ≦ N-1)$ * The given graph is a tree. ## Input The input is given from Standard Input in the following format: $N$ $a_1$ $b_1$ : $a_{N-1}$ $b_{N-1}$ [samples]

Samples

Input #1

Output #1

2

A 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 $2$.
A 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 $7$.
A 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 $6$.

Input #2

Output #2

API Response (JSON)

{
  "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 mor...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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