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.lang.reflect.Array;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;
 
public class Main {
	private InputStream is;
	private PrintWriter out;
	int time = 0, dp[][], DP[][], dist[], prime[], start[], parent[], end[],
			val[], black[], arr[], arr1[][];
	long MOD = (long) (1e9 + 9);
	ArrayList<Integer>[] amp;
	boolean b[], b1[];
	Pair prr1[];
	char ch[][], c[];
	HashSet<Integer> hs1 = new HashSet<>(), hs2 = new HashSet<>();
 
	public static void main(String[] args) throws Exception {
		new Thread(null, new Runnable() {
			public void run() {
				try {
 
					// new Main().soln();
				} catch (Exception e) {
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
		new Main().soln();
	}
 
	int MAX = 1000010, N, K;
	double Q = 1;
	double a = 1 , fa = 0;
	long B = 0;
	PriorityQueue<Pair> pq;
	int Dp[][] = new int[1010][1010];
	int MOD1 = 1000000007, MOD2 = 1000000009;
	void solve() {
		int n = ni();
		amp = (ArrayList<Integer>[]) new ArrayList[n];
		for(int i = 0;i<n; i++) amp[i] = new ArrayList<>();
		buildGraph(n-1);
		b = new boolean[n];
		parent = new int[n];
		dist = new int[n];
		parent[0] = -1;
		int temp = n-1;
		int cnt = 0;
		dfs(0);
		while(parent[temp]!=0){
			cnt++;
			temp = parent[temp];
		}
		cnt+=dist[n-1];
		//System.out.println(cnt);
		if(cnt>=(n-cnt)){
			System.out.println("Snuke");
		}
		else System.out.println("Fennec");
	}
	int dfs(int x){
		b[x] = true;
		for(int i:amp[x]){
			if(!b[i]){
				parent[i] = x;
				dist[x] += dfs(i);
			}
		}
		return (++dist[x]);
	}
	void buildGraph(int n){
		while(n-->0){
			int x= ni()-1, y = ni()-1;
			amp[x].add(y);
			amp[y].add(x);
		}
	}
	void recur(int x, int y, int p){
		int val = 0;
		if(x>y || y<x) return;
		if(x>0){
			if(p==1){
				val = arr[x]-arr[x-1];
			}
			if(p==3){
				if(arr[x]-arr[x-1]<K){
					recur(x+1,y,3);
				}
				else val = arr[x]-arr[x-1];
			}
		}
		if(y<N){
			if(p==4){
				B += arr[y+1]-arr[y];
			}
			if(p==2){
				if(arr[y+1]-arr[y]<K){
					recur(x,y-1,2);
				}
				else val = arr[y+1]-arr[y];
			}
		}
		B += val;
		if(x==y){
			System.out.println(B+" "+a);
			fa += B*a;
		}
		//System.out.println(Q);
		a*=Q;
		recur(x+1,y,1);
		recur(x,y-1,2);
		a/=Q;
		a*=(1-Q);
		recur(x+1,y,3);
		recur(x,y-1,4);
		a/=(1-Q);
		B -= val;
		//System.out.println(a+" "+B);
	}
	class cell implements Comparable<cell>{
		char ch;
		int i;
		cell(char c, int x){
			ch = c;
			i = x;
		}
		public boolean equals(Object o) {
			cell other = (cell) o;
			return ((ch == other.ch && i == other.i));// || (v == other.u && u ==
			// other.v));
		}
		@Override
		public int compareTo(cell c) {
			if(this.ch<c.ch) return -1;
			if(this.ch==c.ch) {
				if(this.i<c.i)return 1;
				if(this.i==c.i) return 0;
				return -1;
			}
			return 1;
		}
 
		public String toString() {
			return "[u=" + ch + ", v=" + i + "]";
		}
		
	}
	int T[] = new int[100010], L[] = new int[100010];
	int P[][] = new int[100010][30];
 
	void process3(int N) {
		int i, j;
 
		// we initialize every element in P with -1
		for (i = 0; i < N; i++)
			for (j = 0; 1 << j < N; j++)
				P[start[i]][j] = -1;
 
		// the first ancestor of every node i is T[i]
		for (i = 0; i < N; i++)
			P[start[i]][0] = T[i];
 
		// bottom up dynamic programing
		for (j = 1; 1 << j < N; j++)
			for (i = 0; i < N; i++)
				if (P[start[i]][j - 1] != -1)
					P[start[i]][j] = P[P[start[i]][j - 1]][j - 1];
	}
 
	int query(int p, int q) {
		int tmp = 0, log = 0, i = 0;
 
		// if p is situated on a higher level than q then we swap them
		if (L[p] < L[q])
			tmp = p;
		p = q;
		q = tmp;
 
		// we compute the value of [log(L[p)]
		for (log = 1; 1 << log <= L[p]; log++)
			;
		log--;
 
		// we find the ancestor of node p situated on the same level
		// with q using the values in P
		for (i = log; i >= 0; i--)
			if (L[p] - (1 << i) >= L[q])
				p = P[p][i];
 
		if (p == q)
			return p;
 
		// we compute LCA(p, q) using the values in P
		for (i = log; i >= 0; i--)
			if (P[p][i] != -1 && P[p][i] != P[q][i])
				p = P[p][i];
		q = P[q][i];
 
		return T[p];
	}
 
 
	long ans = 0;
 
	void recur(int i, int k, long sum) {
		if (k > K)
			return;
		if (k == K) {
			ans = Math.max(ans, sum);
		}
		for (int j = i; j < N; j++) {
 
			recur(j + 1, k + 1, sum);
		}
	}
 
	long[] mul(long arr[][], long temp[]) {
		long ans[] = new long[temp.length];
		for (int i = 0; i < arr.length; i++) {
			long sum = 0;
			for (int j = 0; j < arr.length; j++) {
				sum = (sum + arr[i][j] * temp[j]) % MOD;
			}
			ans[i] = sum;
		}
		return ans;
	}
 
	void printMat(long arr[][]) {
		for (int i = 0; i < arr.length; i++) {
			for (int j = 0; j < arr.length; j++) {
				System.out.print(arr[i][j] + " ");
			}
			System.out.println();
		}
		System.out.println("-----");
	}
 
	void printMat(long arr[]) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		System.out.println("-----");
	}
 
	long[][] matMul(int n, long arr[][], long y) {
		long iden[][] = new long[n][n];
		for (int i = 0; i < n; i++)
			iden[i][i] = 1;
		// printMat(iden);
		while (y > 0) {
			if (y % 2 == 1) {
				iden = mul(n, iden, arr);
				// printMat(iden);
				y--;
			} else {
				arr = mul(n, arr, arr);
				// printMat(arr);
				y /= 2;
			}
		}
		return iden;
	}
 
	long[][] mul(int n, long a1[][], long a2[][]) {
		long temp[][] = new long[n][n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				long sum = 0;
				for (int k = 0; k < n; k++) {
					sum = (sum + a1[i][k] * a2[k][j]) % MOD;
				}
				temp[i][j] = sum;
			}
		}
		return temp;
	}
 
	void seive(int n) {
		b = new boolean[n + 1];
		prime = new int[n + 1];
		for (int i = 2; i * i <= n; i++) {
			if (!b[i]) {
				for (int j = 2 * i; j <= n; j += i) {
					if (!b[j]) {
						b[j] = true;
						prime[j] = i;
					}
				}
			}
		}
	}
 
	int binarySearch1(int arr[], int x) {
		int ans = -1;
		int low = 0, high = arr.length - 1;
		while (high >= low) {
			int mid = (low + high) / 2;
			if (arr[mid] >= x) {
				ans = mid;
				high = mid - 1;
			} else
				low = mid + 1;
		}
		return ans;
	}
 
	int binarySearch2(Integer arr[], int x) {
		int ans = -1;
		int low = 0, high = arr.length - 1;
		while (high >= low) {
			int mid = (low + high) / 2;
			if (arr[mid] >= x) {
				ans = mid;
				low = mid + 1;
			} else
				high = mid - 1;
		}
		return ans + 1;
	}
 
	int cntEven(String str) {
		int cnt = 0;
		for (int i = str.length() - 1; i >= 0; i--) {
			if ((str.charAt(i) - '0') % 2 == 0) {
				cnt++;
			}
		}
		return cnt;
	}
 
	int max = 0;
 
	int getParent(int x) {
		// System.out.println(x+" "+parent[x]);
		if (parent[x] != x) {
			parent[x] = getParent(parent[x]);
		}
		return parent[x];
	}
 
	class Pair implements Comparable<Pair> {
		int u;
		int v, r, i;
 
		Pair(int u, int v, int r, int i) {
			this.u = u;
			this.v = v;
			this.r = r;
			this.i = i;
		}
 
		Pair(int u, int v, int r) {
			this.u = u;
			this.v = v;
			this.r = r;
		}
 
		Pair(int u, int v) {
			this.u = u;
			this.v = v;
		}
 
		public int hashCode() {
			return Objects.hash();
		}
 
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return ((u == other.u && v == other.v));// || (v == other.u && u ==
			// other.v));
		}
 
		public int compareTo(Pair other) {
			//return Long.compare(r, other.r);
			 return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u))
			 : (Long.compare(v, other.v));
			// :(Long.compare(other.r, r))) ;
		}
 
	}
 
	int min(int x, int y) {
		if (x < y)
			return x;
		return y;
	}
 
	int max(int x, int y) {
		if (x > y)
			return x;
		return y;
	}
 
 
	long modInverse(long a, long mOD2) {
		return power(a, mOD2 - 2, mOD2);
	}
 
	long power(long x, long y, long m) {
		if (y == 0)
			return 1;
		long p = power(x, y / 2, m) % m;
		p = (p * p) % m;
 
		return (y % 2 == 0) ? p : (x * p) % m;
	}
 
	boolean isPrime(int x) {
		for (int i = 2; i * 1L * i <= x; i++)
			if (x % i == 0)
				return false;
		return true;
	}
 
	public long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}
 
	void failFn(String str, int arr[]) {
		int len = 0;
		arr[0] = 0;
		int i = 1;
		while (i < arr.length) {
			if (str.charAt(i) == str.charAt(len)) {
				arr[i++] = ++len;
				continue;
			}
			if (len == 0) {
				arr[i] = len;
				i++;
				continue;
			}
			if (str.charAt(i) != str.charAt(len)) {
				len = arr[len - 1];
			}
		}
	}
 
	static class ST1 {
		int arr[], st[], size;
 
		ST1(int a[]) {
			arr = a.clone();
			size = 10 * arr.length;
			st = new int[size];
			build(0, arr.length - 1, 1);
		}
 
		void build(int ss, int se, int si) {
			if (ss == se) {
				st[si] = arr[ss];
				return;
			}
			int mid = (ss + se) / 2;
			int val = 2 * si;
			build(ss, mid, val);
			build(mid + 1, se, val + 1);
			st[si] = (st[val] + st[val + 1]);
		}
 
		int get(int ss, int se, int l, int r, int si) {
			if (l > se || r < ss || l > r)
				return Integer.MAX_VALUE;
			if (l <= ss && r >= se)
				return st[si];
			int mid = (ss + se) / 2;
			int val = 2 * si;
			return (get(ss, mid, l, r, val) + get(mid + 1, se, l, r, val + 1));
		}
	}
 
	static class ST {
		int arr[], lazy[], n;
 
		ST(int a) {
			n = a;
			arr = new int[10 * n];
			lazy = new int[10 * n];
		}
 
		void up(int l, int r, int val) {
			update(0, n - 1, 0, l, r, val);
		}
 
		void update(int l, int r, int c, int x, int y, int val) {
			if (lazy[c] != 0) {
				lazy[2 * c + 1] ^= lazy[c];
				lazy[2 * c + 2] ^= lazy[c];
				if (l == r)
					arr[c] ^= lazy[c];
				lazy[c] = 0;
			}
			if (l > r || x > y || l > y || x > r)
				return;
			if (x <= l && y >= r) {
				if ((r - l + 1) % 2 == 1)
					lazy[c] ^= val;
				return;
			}
			int mid = l + r >> 1;
		update(l, mid, 2 * c + 1, x, y, val);
		update(mid + 1, r, 2 * c + 2, x, y, val);
		arr[c] = (arr[2 * c + 1] + arr[2 * c + 2]);
		}
 
		int an(int ind) {
			return ans(0, n - 1, 0, ind);
		}
 
		int ans(int l, int r, int c, int ind) {
			if (lazy[c] != 0) {
				lazy[2 * c + 1] += lazy[c];
				lazy[2 * c + 2] += lazy[c];
				if (l == r)
					arr[c] += lazy[c];
				lazy[c] = 0;
			}
			if (l == r)
				return arr[c];
			int mid = l + r >> 1;
		if (mid >= ind)
			return ans(l, mid, 2 * c + 1, ind);
		return ans(mid + 1, r, 2 * c + 2, ind);
		}
	}
	static long[] array;
	public static class FenwickTree {
 
		 // 1-indexed array, In this array We save cumulative
		// information to perform efficient range queries and
		// updates
 
		public FenwickTree(int size) {
			array = new long[size + 1];
		}
		int getSum(int index)
		{
			int sum = 0; // Iniialize result
 
			// index in BITree[] is 1 more than the index in arr[]
			index = index + 1;
 
			// Traverse ancestors of BITree[index]
			while (index>0)
			{
				// Add current element of BITree to sum
				sum ^= array[index];
 
				// Move index to parent node in getSum View
				index -= index & (-index);
			}
			return sum;
		}
		public long rsq(int ind) {
			assert ind > 0;
			long sum = 0;
			ind = ind+1;
			while (ind > 0) {
				sum ^= array[ind];
				// Extracting the portion up to the first significant one of the
				// binary representation of 'ind' and decrementing ind by that
				// number
				ind -= ind & (-ind);
			}
			return sum;
		}
 
		public long rsq(int a, int b) {
			assert b >= a && a > 0 && b > 0;
			return rsq(b) ^ rsq(a - 1);
		}
 
		public void update(int ind, long value) {
			assert ind > 0;
			ind = ind+1;
			while (ind < array.length) {
				array[ind] ^= value;
				// Extracting the portion up to the first significant one of the
				// binary representation of 'ind' and incrementing ind by that
				// number
				ind += ind & (-ind);
			}
		}
 
		public int size() {
			return array.length - 1;
		}
	}
 
	public static int[] shuffle(int[] a, Random gen) {
		for (int i = 0, n = a.length; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			int d = a[i];
			a[i] = a[ind];
			a[ind] = d;
		}
		return a;
	}
 
	long power(long x, long y, int mod) {
		long ans = 1;
		while (y > 0) {
			if (y % 2 == 0) {
				x = (x * x) % mod;
				y /= 2;
			} else {
				ans = (x * ans) % mod;
				y--;
			}
		}
		return ans;
	}
 
	void soln() {
		is = System.in;
		out = new PrintWriter(System.out);
		long s = System.currentTimeMillis();
		solve();
		out.close();
		out.flush();
		tr(System.currentTimeMillis() - s + "ms");
	}
 
	// To Get Input
	// Some Buffer Methods
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
 
	private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}
 
	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}
 
	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}
 
	private double nd() {
		return Double.parseDouble(ns());
	}
 
	private char nc() {
		return (char) skip();
	}
 
	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
			// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
 
	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
 
	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}
 
	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}
 
	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}
 
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
 
	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}
 
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
 
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
 
	private void tr(Object... o) {
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}