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: Accepted)

import java.util.*;
import static java.lang.Math.*;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		Graph g = new Graph(n, false);
		for(int i = 0; i < n-1; i++){
		    int a = sc.nextInt() - 1;
		    int b = sc.nextInt() - 1;
		    g.add(a, b);
		}
		
		// 計算
		String result = "Snuke";
		long[] distFromB = g.bfs(0);
		long[] distFromW = g.bfs(n-1);
		int cnt = 0;
		for(int i = 0; i < n; i++){
		    if(distFromB[i] <= distFromW[i]) cnt++;
		}
		if(cnt > (n-cnt)) result = "Fennec";
		
		// 出力
		System.out.println(result);
	}

}

class Graph {
	int n;
	boolean directed;
	ArrayList<Edge>[] adjList;
	int m;
	long[] dist;
	long[][] distWF;
	int start;
	int[] prev;
	ArrayList<Integer> path;
	long INF = 1001001001001001001L;

	public Graph (int n, boolean directed) {
		this.n = n;
		this.m = 0;
		this.directed = directed;
		this.adjList = new ArrayList[n];
		for(int i = 0; i < n; i++){
			adjList[i] = new ArrayList<Edge>();
		}
	}
	
	public void add(int from, int to) {
		add(from, to, 1);
	}
	public void add(int from, int to, int w) {
		adjList[from].add(new Edge(from, to, w));
		this.m++;
		if(!directed){
			adjList[to].add(new Edge(to, from, w));
			this.m++;
		}
	}
	
	public long[] bfs(int start) { // O(M)
		this.start = start;
		this.prev = new int[n];
		Arrays.fill(prev, -1);
		prev[start] = start;
		this.dist = new long[n];
		Arrays.fill(dist, INF);
		dist[start] = 0;
		ArrayDeque<Integer> q = new ArrayDeque<Integer>();
		q.add(start);
		while(!q.isEmpty()){
			int now = q.poll();
			for(Edge e : adjList[now]){
				if(dist[e.to] != INF) continue;
				dist[e.to] = dist[now] + e.w;
				prev[e.to] = now;
				q.add(e.to);
			}
		}
		return dist;
	}
	
	public long[] dijkstra(int start) { // O(MlogM)
		this.start = start;
		this.prev = new int[n];
		Arrays.fill(prev, -1);
		prev[start] = start;
		this.dist = new long[n];
		Arrays.fill(dist, INF);
		dist[start] = 0;
		PriorityQueue<Vertex> q = new PriorityQueue<Vertex>((x, y) -> Long.compare(x.distance, y.distance));
		q.add(new Vertex(start, 0));
		while(!q.isEmpty()){
			Vertex now = q.poll();
			if(now.distance > dist[now.id]) continue; 
			for(Edge e : adjList[now.id]){
				long newDist = now.distance + e.w;
				if(dist[e.to] <= newDist) continue;
				dist[e.to] = newDist;
				prev[e.to] = now.id;
				q.add(new Vertex(e.to, newDist));
			}
		}
		return dist;
	}
	
	public long[][] wf() { // O(N^3)
		this.distWF = new long[n][n];
		for(int i = 0; i < n; i++){
			Arrays.fill(distWF[i], INF);
			distWF[i][i] = 0;
		}
		for(ArrayList<Edge> list : adjList){
			for(Edge e : list){
				distWF[e.from][e.to] = e.w;
			}
		}
		for(int k = 0; k < n; k++){
			for(int i = 0; i < n; i++){
				for(int j = 0; j < n; j++){
					distWF[i][j] = min(distWF[i][j], distWF[i][k] + distWF[k][j]);
				}
			}
		}
		return distWF;
	}
	
	public boolean bf(int start) { // O(NM)
		this.start = start;
		this.prev = new int[n];
		Arrays.fill(prev, -1);
		prev[start] = start;
		this.dist = new long[n];
		Arrays.fill(dist, INF);
		dist[start] = 0;
		boolean hasNegativeLoop = false;
		for(int i = 0; i < n; i++){
			for(int j = 0; j < n; j++){
				for(Edge e : adjList[j]){
					if(dist[e.to] <= dist[e.from] + e.w) continue;
					dist[e.to] = dist[e.from] + e.w;
					prev[e.to] = e.from;
					if(i == n-1) hasNegativeLoop = true;
				}
			}
		}
		return hasNegativeLoop;
	}
	
	public ArrayList<Integer> pathTo(int to){
		this.path = new ArrayList<Integer>();
		return pathToRec(to);
	}
	
	private ArrayList<Integer> pathToRec(int to){
		if(to != start) pathToRec(prev[to]);
		path.add(to);
		return path;
	}
	
	public String toString(){
		StringBuilder sb = new StringBuilder();
		for(ArrayList<Edge> list : adjList){
			for(Edge e : list){
				sb.append(e.toString());
				sb.append("\n");
			}
		}
		return sb.toString();
	}
	
	public String distToString(){
		if(dist != null) return Arrays.toString(dist);
		StringBuilder sb = new StringBuilder();
		for(int i = 0; i < n; i++){
			for(int j = 0; j < n; j++){
				if(distWF[i][j] == INF){
					sb.append("from:" + i + " to:" + j + " dist:INF" + "\n");
				}else{
					sb.append("from:" + i + " to:" + j + " dist:" + distWF[i][j] + "\n");
				}
			}
		}
		return sb.toString();
	}
	
	class Edge {
		int from;
		int to;
		int w;
		
		Edge(int from, int to, int w){
			this.from = from;
			this.to = to;
			this.w = w;
		}
		
		public String toString(){
			return "from:" + from + " to:" + to + " w:" + w;
		}
	}
	
	class Vertex {
		int id;
		long distance;
		
		Vertex(int id, long distance){
			this.id = id;
			this.distance = distance;
		}
		
		public String toString(){
			return "id:" + id + " distance:" + distance;
		}
	}
}