Removing Coins

AtCoder

IDagc033_c

Time2000ms

Memory256MB

Difficulty—

Takahashi and Aoki will play a game on a tree. The tree has $N$ vertices numbered $1$ to $N$, and the $i$\-th of the $N-1$ edges connects Vertex $a_i$ and Vertex $b_i$. At the beginning of the game, each vertex contains a coin. Starting from Takahashi, he and Aoki will alternately perform the following operation: * Choose a vertex $v$ that contains one or more coins, and remove all the coins from $v$. * Then, move each coin remaining on the tree to the vertex that is nearest to $v$ among the adjacent vertices of the coin's current vertex. The player who becomes unable to play, loses the game. That is, the player who takes his turn when there is no coin remaining on the tree, loses the game. Determine the winner of the game when both players play optimally. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq a_i, b_i \leq N$ * $a_i \neq b_i$ * The graph given as input is a tree. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $b_1$ $a_2$ $b_2$ $:$ $a_{N-1}$ $b_{N-1}$ [samples]

Samples

Input #1

3
1 2
2 3

Output #1

First

Here is one possible progress of the game:

*   Takahashi removes the coin from Vertex $1$. Now, Vertex $1$ and Vertex $2$ contain one coin each.
*   Aoki removes the coin from Vertex $2$. Now, Vertex $2$ contains one coin.
*   Takahashi removes the coin from Vertex $2$. Now, there is no coin remaining on the tree.
*   Aoki takes his turn when there is no coin on the tree and loses.

Input #2

Output #2

Second

Input #3

Output #3

First

API Response (JSON)

{
  "problem": {
    "name": "Removing Coins",
    "description": {
      "content": "Takahashi and Aoki will play a game on a tree. The tree has $N$ vertices numbered $1$ to $N$, and the $i$\\-th of the $N-1$ edges connects Vertex $a_i$ and Vertex $b_i$. At the beginning of the game, e",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc033_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi and Aoki will play a game on a tree. The tree has $N$ vertices numbered $1$ to $N$, and the $i$\\-th of the $N-1$ edges connects Vertex $a_i$ and Vertex $b_i$.\nAt the beginning of the game, e...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments