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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;
using System.Numerics;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            var N = cin.ReadInt;
            var abs = new int[N-1].Select(x => cin.ReadLine.Split(' ').Select(y => int.Parse(y)).ToArray());
            var points = new int[N + 1].Select(x => new List<int>()).ToArray(); // 0 は使用しない

            foreach (var ab in abs)
            {
                points[ab[0]].Add(ab[1]);
                points[ab[1]].Add(ab[0]);
            }

            var queOfFennec = new Queue<int>();
            var queOfSnuke = new Queue<int>();

            Func<int, int, List<int>, List<int>> GetRoot = null;
            GetRoot = (int pre, int now, List<int> root) =>
            {
                var newlist = new List<int>(root);
                newlist.Add(now);
                if (now == N) return newlist;

                foreach (var p in points[now])
                {
                    if (p == pre) continue;
                    var wk = GetRoot(now, p, newlist);
                    if (wk.Count != 0) return wk;
                }
                return new List<int>();
            };

            var root = GetRoot(-1, 1, new List<int>());


            //WriteLine("--------- line 1 -----------");
            //root.ForEach(x => WriteLine(x));
            root.ForEach(x => queOfFennec.Enqueue(x));
            root.Reverse();
            //WriteLine("--------- line 2 -----------");
            //root.ForEach(x => WriteLine(x));
            root.ForEach(x => queOfSnuke.Enqueue(x));

            var isRooted = new int[N+1];
            var countOfFennec = 0;
            var countOfSnuke = 0;
            //WriteLine("--------------------");
            while (true) 
            {
                while(true)
                {
                    if (queOfFennec.Count == 0) break;
                    var f = queOfFennec.Dequeue();
                    //WriteLine("f {0} {1}", f, countOfFennec);
                    if (isRooted[f] == 1) continue;
                    foreach (var p in points[f])
                    {
                        queOfFennec.Enqueue(p);
                    }
                    isRooted[f] = 1;
                    countOfFennec++;
                    break;
                }

                while (true)
                {
                    if (queOfSnuke.Count == 0) break;
                    var s = queOfSnuke.Dequeue();
                    //WriteLine("s {0} {1}", s, countOfSnuke);
                    if (isRooted[s] == 1) continue;
                    foreach (var p in points[s])
                    {
                        queOfSnuke.Enqueue(p);
                    }
                    isRooted[s] = 1;
                    countOfSnuke++;
                    break;
                }
                if (countOfSnuke != countOfFennec) break;
            }

            WriteLine(countOfFennec > countOfSnuke ? "Fennec" : "Snuke");
        }

        private BigInteger Lcm(BigInteger a, BigInteger b)
        {
            return (a * b) / Gcd(a, b);
        }

        /// <summary>
        /// 最大公約数計算
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        private BigInteger Gcd(BigInteger a, BigInteger b)
        {
            if (a < b) return Gcd(b, a);

            while (b != 0)
            {
                var mod = a % b;
                a = b;
                b = mod;
            }
            return a;
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; i++)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }

        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }

    /// <summary>
    /// Mod計算用クラス
    /// </summary>
    struct ModInt
    {
        const int M = 1000000007;
        public long V;
        public ModInt(long v) { V = (v %= M) < 0 ? v + M : v; }

        public static implicit operator ModInt(long v) => new ModInt(v);
        public static ModInt operator +(ModInt x) => x;
        public static ModInt operator -(ModInt x) => -x.V;
        public static ModInt operator +(ModInt x, ModInt y) => x.V + y.V;
        public static ModInt operator -(ModInt x, ModInt y) => x.V - y.V;
        public static ModInt operator *(ModInt x, ModInt y) => x.V * y.V;
        public static ModInt operator /(ModInt x, ModInt y) => x.V * y.Inv();

        public ModInt Pow(int i) => MPow(V, i);
        public ModInt Inv() => MPow(V, M - 2);
        public override string ToString() => $"{V}";

        static long MPow(long b, int i)
        {
            for (var r = 1L; ; b = b * b % M)
            {
                if (i % 2 > 0) r = r * b % M;
                if ((i /= 2) < 1) return r;
            }
        }

        public static long MFactorial(int n) { for (long x = 1, i = 1; ; x = x * ++i % M) if (i >= n) return x; }
        public static long MNpr(int n, int r)
        {
            if (n < r) return 0;
            for (long x = 1, i = n - r; ; x = x * ++i % M) if (i >= n) return x;
        }
        public static ModInt MNcr(int n, int r) => n < r ? 0 : n - r < r ? MNcr(n, n - r) : (ModInt)MNpr(n, r) / MFactorial(r);
    }
}