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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {

    private static int N;
    private static int[] A;
    private static int[] B;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        N = sc.nextInt();
        A = new int[N];
        B = new int[N];
        for (int i = 0; i < N-1; i++) {
            A[i] = sc.nextInt();
            B[i] = sc.nextInt();
        }
        System.out.println(solve());
    }

    private static String solve() {
        Rin r = mkRin();
        Path path = findPath(r);

        List<Integer> nodes = path.nodes;

        boolean fene = true;
        while(nodes.size() > 2) {
            if( fene ) {
                nodes.remove(0);
                fene = false;
            } else {
                nodes.remove(nodes.size() - 1);
                fene = true;
            }
        }

        int cut1 = nodes.get(0);
        int cut2 = nodes.get(1);

        UnionFind uf = new UnionFind(N);
        for (int i = 0; i < N-1; i++) {
            int a = A[i];
            int b = B[i];

            if( cut1 == a && cut2 == b || cut1 == b && cut2 == a ) {
                continue;
            }

            uf.unite(a-1, b-1);
        }

        int fRoot = uf.root(0);
        int f = 0;
        for (int i = 0; i < N; i++) {
            if( uf.root(i) == fRoot ) {
                f++;
            }
        }

        int s = N - f;

        if( f > s ) {
            return "Fennec";
        } else {
            return "Snuke";
        }
    }

    private static Path findPath(Rin r) {
        boolean[] used = new boolean[N];
        List<Path> current = Collections.singletonList(Path.single(1));
        while(true) {
            List<Path> next = new ArrayList<>();
            for (Path path : current) {
                for (Integer n : r.get(path.last())) {
                    if( n == N ) {
                        return path.add(n);
                    } else if( !used[n] ){
                        next.add(path.add(n));
                        used[n] = true;
                    }
                }
            }
            current = next;
        }
    }

    private static Rin mkRin() {
        Rin r = new Rin(N);
        for (int i = 0; i < N-1; i++) {
            r.set(A[i], B[i]);
        }
        return r;
    }

    // 隣接リスト
    private static class Rin {

        private final List[] array;

        public Rin(int n) {
            array = new List[n];
        }

        public void set(int a, int b) {
            get(a).add(b);
            get(b).add(a);
        }

        public List<Integer> get(int n) {
            if( array[n - 1] == null ) {
                array[n - 1] = new ArrayList();
            }
            //noinspection unchecked
            return (List<Integer>)array[n - 1];
        }
    }

    public static class Path {

        public static Path single(int n) {
            return new Path(Collections.singletonList(n));
        }

        private final List<Integer> nodes;

        public Path(List<Integer> nodes) {
            this.nodes = nodes;
        }

        public Path add(int n) {
            List<Integer> list = new ArrayList<>(nodes.size() + 1);
            list.addAll(nodes);
            list.add(n);
            return new Path(list);
        }

        public int last() {
            return nodes.get(nodes.size() - 1);
        }
    }

    static class UnionFind {

        private int[] parent;
        private int[] rank;

        public UnionFind(int n) {
            parent = new int[n];
            rank = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
                rank[i] = 0;
            }
        }

        int root(int n) {
            if( parent[n] == n ) {
                return n;
            } else {
                parent[n] = root(parent[n]);
                return parent[n];
            }
        }

        void unite(int x, int y) {
            x = root(x);
            y = root(y);
            if( x == y ) return;

            if( rank[x] < rank[y] ) {
                parent[x] = y;
            } else {
                parent[y] = x;
                if( rank[x] == rank[y]) rank[x]++;
            }
        }
    }
}