Problem:
Score : 400 points

Problem Statement

Fennec and Snuke are playing a board game.

On the board, there are N cells numbered 1 through N, and N-1 roads, each connecting two cells. Cell a_i is adjacent to Cell b_i through the i-th road. Every cell can be reached from every other cell by repeatedly traveling to an adjacent cell. In terms of graph theory, the graph formed by the cells and the roads is a tree.

Initially, Cell 1 is painted black, and Cell N is painted white. The other cells are not yet colored.
Fennec (who goes first) and Snuke (who goes second) alternately paint an uncolored cell.
More specifically, each player performs the following action in her/his turn:

Fennec: selects an uncolored cell that is adjacent to a black cell, and paints it black.

Snuke: selects an uncolored cell that is adjacent to a white cell, and paints it white.

A player loses when she/he cannot paint a cell. Determine the winner of the game when Fennec and Snuke play optimally.

Constraints

2 \leq N \leq 10^5

1 \leq a_i, b_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}

Output

If Fennec wins, print Fennec; if Snuke wins, print Snuke.

Sample Input 1

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

Sample Output 1

Fennec

For example, if Fennec first paints Cell 2 black, she will win regardless of Snuke's moves.

Sample Input 2

4
1 4
4 2
2 3

Sample Output 2

Snuke

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

//#pragma warning disable

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

public class Test
{
    public class Tree
    {
        public Node Root;
        public Node[] Leaves;  // 注意：根はLeavesに含まれません

        public Tree(IEnumerable<long>[] adjacency_list)
        {
            Root = FromAdjacencyList(adjacency_list, 0, null);

            Leaves = SearchLeaves(Root).ToArray();
        }

        public IEnumerable<Node> Nodes
        {
            get { return Root.Nodes; }
        }

        public override string ToString()
        {
            return Root.ToString();
        }

        private IEnumerable<Node> SearchLeaves(Node v)
        {
            if (v.Children.Length == 0)
            {
                return new[] { v };
            }

            var ret = new List<Node>();

            foreach (var c in v.Children)
            {
                ret.AddRange(SearchLeaves(c));
            }

            return ret;
        }

        private static Node FromAdjacencyList(IEnumerable<long>[] adjacency_list, long rootIndex = 0, long? parentIndex = null)
        {
            var children = adjacency_list[rootIndex]
                .Where(x => x != parentIndex)
                .Select(x => FromAdjacencyList(adjacency_list, x, rootIndex))
                .ToArray();

            var root = new Node(null, children, rootIndex);

            foreach (var c in children)
            {
                c.Parent = root;
            }

            return root;
        }

        public class Node
        {
            public Node Parent;
            public Node[] Children;
            public long Id;
            public int Degree { get { return Children.Length; } }  // 注意：親への辺は数に含みません

            public Node(Node parent, Node[] children, long id) { Parent = parent; Children = children; Id = id; }

            public override string ToString()
            {
                return Id + (Children.Length == 0 ? "" : "[" + string.Join(",", Children.Select(x => x.ToString())) + "]");
            }

            public IEnumerable<Node> Nodes
            {
                get
                {
                    yield return this;

                    foreach (var c in Children)
                    {
                        foreach (var v in c.Nodes)
                        {
                            yield return v;
                        }
                    }
                }
            }
        }
    }

    public static void Main()
    {
        var N = long.Parse(Console.ReadLine());

        var adj = new List<long>[N];
        for (int i = 0; i < N; i++)
        {
            adj[i] = new List<long>();
        }

        for (var i = 0; i < N - 1; i++)
        {
            var line1 = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();

            adj[line1[0] - 1].Add(line1[1] - 1);
            adj[line1[1] - 1].Add(line1[0] - 1);
        }
        
        //*** 1 から N までのパスを見つける ***
        long[] prev = new long[N];
        bool finished = false;

        Queue<long> q = new Queue<long>();
        foreach (var child in adj[0])
        {
            q.Enqueue(child);
            prev[child] = 0;  // root

            if (child == N - 1)
            {
                finished = true;
                break;
            }
        }

        while (!finished)
        {
            var node = q.Dequeue();
            foreach (var child in adj[node])
            {
                q.Enqueue(child);
                prev[child] = node;

                if (child == N - 1)
                {
                    finished = true;
                    break;
                }
            }
        }

        //*** 1 から N までのパスをリストに格納
        List<long> myPath = new List<long>();
        long next = N - 1;
        while (next != 0)
        {
            myPath.Add(next);
            next = prev[next];
        }
        myPath.Add(0);
        myPath.Reverse();  // 1 から N へ

        //Console.WriteLine(string.Join(",", myPath.Select(x => x + "").ToArray()));

        //*** 最適な戦略で挑戦する ***
        var player1Queue = new Queue<long>();
        var player2Queue = new Queue<long>();
        bool[] filled = new bool[N];
        int player1ptr = 0;
        int player2ptr = 0;

        for (int i = 0; i < (myPath.Count + 1) / 2; i++)
        {
            player1Queue.Enqueue(myPath[i]);
            filled[myPath[i]] = true;
            player1ptr++;
        }

        for (int i = (myPath.Count + 1) / 2; i < myPath.Count; i++)
        {
            player2Queue.Enqueue(myPath[i]);
            filled[myPath[i]] = true;
            player2ptr++;
        }


        while (player1Queue.Count != 0)
        {
            var next2 = player1Queue.Dequeue();

            foreach (var child in adj[next2])
            {
                if (filled[child] == false)
                {
                    filled[child] = true;
                    player1ptr++;
                    player1Queue.Enqueue(child);
                }
            }
        }
        
        while (player2Queue.Count != 0)
        {
            var next2 = player2Queue.Dequeue();

            foreach (var child in adj[next2])
            {
                if (filled[child] == false)
                {
                    filled[child] = true;
                    player2ptr++;
                    player2Queue.Enqueue(child);
                }
            }
        }

        //Console.WriteLine(player1ptr);
        //Console.WriteLine(player2ptr);

        Console.WriteLine((player1ptr <= player2ptr) ? "Snuke" : "Fennec");
    }
}