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: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int n = sc.nextInt();

		List<List<Integer>> edges = new ArrayList<>(n);
		for (int i = 0; i < n; i++) {
			edges.add(new ArrayList<>());
		}

		for (int i = 0; i < n - 1; i++) {
			int a = sc.nextInt() - 1;
			int b = sc.nextInt() - 1;

			edges.get(a).add(b);
			edges.get(b).add(a);
		}

		int[] cnt = new int[n];
		int[] p = new int[n];
		boolean[] f = new boolean[n];
		Arrays.fill(p, -1);
		boolean[] used = new boolean[n];
		boolean[] used2 = new boolean[n];
		Deque<Integer> st = new ArrayDeque<>();
		st.push(0);
		p[0] = 0;
		while (!st.isEmpty()) {
			int e = st.peek();

			if (used[e]) {
				st.pop();
			} else if (used2[e]) {
				st.pop();
				used[e] = true;

				cnt[e]++;
				cnt[p[e]] += cnt[e];
				f[p[e]] |= f[e];
			} else {
				used2[e] = true;
				for (int next : edges.get(e)) {
					if (used[next]) {
						continue;
					}
					if (used2[next]) {
						// 後退辺
						continue;
					}
					if (next == n - 1) {
						f[e] = true;
						continue;
					}

					st.push(next);
					p[next] = e;
				}
			}
		}

		final int OFFSET = 1_000_000;
		Arrays.fill(used, false);
		PriorityQueue<Integer> fq = new PriorityQueue<Integer>();
		PriorityQueue<Integer> sq = new PriorityQueue<Integer>();
//		used[0] = true;
		fq.add(0);
//		used[n - 1] = true;
		sq.add(n - 1);

		while (true) {
			while (!fq.isEmpty() && used[fq.peek() % OFFSET]) {
				fq.remove();
			}

			if (fq.isEmpty()) {
				pr.println("Snuke");
				return;
			} else {
				int fe = fq.remove() % OFFSET;
				used[fe] = true;
				for (int next : edges.get(fe)) {
					if (!used[next]) {
						if (!f[next]) {
							fq.add(next + OFFSET);
						} else {
							fq.add(next);
						}
//						used[next] = true;
					}
				}
			}

			while (!sq.isEmpty() && used[sq.peek() % OFFSET]) {
				sq.remove();
			}

			if (sq.isEmpty()) {
				pr.println("Fennec");
				return;
			} else {
				int se = sq.remove() % OFFSET;
				used[se] = true;
				for (int next : edges.get(se)) {
					if (!used[next]) {
						if (!f[next]) {
							sq.add(next + OFFSET);
						} else {
							sq.add(next);
						}
						used[next] = true;
					}
				}
			}
		}
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(System.in);
		pr = new Printer(System.out);

		solve();

		pr.close();
		sc.close();
	}

	@SuppressWarnings("unused")
	private static class Scanner {
		BufferedReader br;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	private static class Printer extends PrintWriter {
		Printer(PrintStream out) {
			super(out);
		}
	}
}