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: Memory Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Deque;
import java.util.HashSet;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.Set;

public class Main {
	public static void main(String args[]) {
		FastScanner scanner = new FastScanner();
		int n=scanner.nextInt();
		int[] a=new int[n-1];
		int[] b=new int[n-1];
		boolean[][] graph=new boolean[n][n];
		for(int i=0;i<n-1;i++){
			a[i]=scanner.nextInt()-1;
			b[i]=scanner.nextInt()-1;
			graph[a[i]][b[i]]=true;
			graph[b[i]][a[i]]=true;
		}
		Deque<Integer>que=new ArrayDeque<>();
		que.add(0);
		Set<Integer>checked=new HashSet<>();
		int[] memo=new int[n];
		while(!que.isEmpty()){
			int tar=que.poll();
			checked.add(tar);
			for(int i=0;i<n;i++){
				if(graph[tar][i]&&!checked.contains(i)){
					que.add(i);
					memo[i]=tar;
				}
			}
		}
		List<Integer>center=new ArrayList<>();
		int pre=memo[n-1];
		center.add(n-1);
		while(true){
			center.add(pre);
			if(pre==0){
				break;
			}
			pre=memo[pre];
		}
		Collections.reverse(center);
		Deque<Integer>queF=new ArrayDeque<>();
		for(int i=0;i<Math.ceil(center.size()/2.0);i++){
			queF.add(center.get(i));
		}
		
		int cntF=0;
		checked=new HashSet<>();
		while(!queF.isEmpty()){
			int tar=queF.poll();
			checked.add(tar);
			for(int i=0;i<n;i++){
				if(graph[tar][i]&&!center.contains(i)&&!checked.contains(i)){
					queF.add(i);
				}
			}
			cntF++;
		}
		int cntS=n-cntF;
		System.out.println(cntF>cntS?"Fennec":"Snuke");
	}
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}