Problem:
Score : 800 points

Problem Statement

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}

Output

Print First if Takahashi will win, and print Second if Aoki will win.

Sample Input 1

3
1 2
2 3

Sample 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.

Sample Input 2

6
1 2
2 3
2 4
4 6
5 6

Sample Output 2

Second

Sample Input 3

7
1 7
7 4
3 4
7 5
6 3
2 1

Sample Output 3

First

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Numerics;
using System.Threading.Tasks;
using System.Text.RegularExpressions;
using static System.Math;
using Debug = System.Diagnostics.Debug;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;

static class P
{
    static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
        ReRooting<int> getDiameter = new ReRooting<int>(n, edges, 0, Max, x => x + 1);
        var diameter = Enumerable.Range(0, n).Select(x => getDiameter.Query(x)).Max() - 1;
        Console.WriteLine(diameter % 3 == 1 ? "Second" : "First");
    }
}


class ReRooting<T>
{
    public int NodeCount { get; private set; }

    int[][] Neighbours;
    int[][] IndexForNeighbours;

    T[] Res;
    T[][] dp;

    T IdentityElement;
    Func<T, T, T> Operate;
    Func<T, T> OperateNode;

    public ReRooting(int nodeCount, int[][] edges, T identityElement, Func<T, T, T> operate, Func<T, T> operateNode)
    {
        NodeCount = nodeCount;

        IdentityElement = identityElement;
        Operate = operate;
        OperateNode = operateNode;

        List<int>[] neighbours = new List<int>[nodeCount];
        List<int>[] indexForNeighbours = new List<int>[nodeCount];

        for (int i = 0; i < nodeCount; i++)
        {
            neighbours[i] = new List<int>();
            indexForNeighbours[i] = new List<int>();
        }
        for (int i = 0; i < edges.Length; i++)
        {
            var edge = edges[i];
            indexForNeighbours[edge[0]].Add(neighbours[edge[1]].Count);
            indexForNeighbours[edge[1]].Add(neighbours[edge[0]].Count);
            neighbours[edge[0]].Add(edge[1]);
            neighbours[edge[1]].Add(edge[0]);
        }

        Neighbours = new int[nodeCount][];
        IndexForNeighbours = new int[nodeCount][];
        for (int i = 0; i < nodeCount; i++)
        {
            Neighbours[i] = neighbours[i].ToArray();
            IndexForNeighbours[i] = indexForNeighbours[i].ToArray();
        }

        dp = new T[Neighbours.Length][];
        Res = new T[Neighbours.Length];

        for (int i = 0; i < Neighbours.Length; i++) dp[i] = new T[Neighbours[i].Length];
        if (NodeCount > 1) Initialize();
        else Res[0] = OperateNode(IdentityElement);
    }

    public T Query(int node) => Res[node];

    private void Initialize()
    {
        int[] parents = new int[NodeCount];
        int[] order = new int[NodeCount];

        #region InitOrderedTree
        var index = 0;
        Stack<int> stack = new Stack<int>();
        stack.Push(0);
        parents[0] = -1;
        while (stack.Count > 0)
        {
            var node = stack.Pop();
            order[index++] = node;
            for (int i = 0; i < Neighbours[node].Length; i++)
            {
                var neighbour = Neighbours[node][i];
                if (neighbour == parents[node]) continue;
                stack.Push(neighbour);
                parents[neighbour] = node;
            }
        }
        #endregion

        #region fromLeaf
        //DFSの逆順に辿ると、親に対して値を返すために必要な情報は既に集まっている。
        for (int i = order.Length - 1; i >= 1; i--)
        {
            var node = order[i];
            var parent = parents[node];

            T accum = IdentityElement;
            int neighbourIndex = -1;
            for (int j = 0; j < Neighbours[node].Length; j++)
            {
                if (Neighbours[node][j] == parent)
                {
                    neighbourIndex = j;
                    continue;
                }
                //部分木の結果を累積
                accum = Operate(accum, dp[node][j]);
            }
            //自ノードの値を作用させ、dpに保持させる
            dp[parent][IndexForNeighbours[node][neighbourIndex]] = OperateNode(accum);
        }
        #endregion

        #region toLeaf
        //既にノードの値を出すために必要な情報は集まっているので、出す
        for (int i = 0; i < order.Length; i++)
        {
            var node = order[i];

            T accum = IdentityElement;

            //尻からの累積
            T[] accumsFromTail = new T[Neighbours[node].Length];
            accumsFromTail[accumsFromTail.Length - 1] = IdentityElement;
            for (int j = accumsFromTail.Length - 1; j >= 1; j--) accumsFromTail[j - 1] = Operate(dp[node][j], accumsFromTail[j]);

            //頭から累積をしながら配る
            for (int j = 0; j < accumsFromTail.Length; j++)
            {
                dp[Neighbours[node][j]][IndexForNeighbours[node][j]] = OperateNode(Operate(accum, accumsFromTail[j]));
                accum = Operate(accum, dp[node][j]);
            }
            Res[node] = OperateNode(accum);
        }
        #endregion
    }
}