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 Kotlin (1.0.0) (judge verdict: Accepted)

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

fun solve(N: Int, a: IntArray, b: IntArray){
    val tree = AdjacentListGraph<Int, Int>(Array(N){ Vertex<Int, Int>() }.toMutableList())
    for(i in 0 until N - 1){
        tree.addEdge(a[i] - 1, b[i] - 1, 1)
        tree.addEdge(b[i] - 1, a[i] - 1, 1)
    }
    val distances1 = tree.getDistances(0)
    val distances2 = tree.getDistances(N - 1)
    val fennec = (0 until N).count{ distances1[it] <= distances2[it] }
    if(fennec > N - fennec){ println("Fennec") }
    else println("Snuke")
    return
}

fun AdjacentListGraph<Int, Int>.getDistances(from: Int): IntArray{
    // Bread First Search
    val distances = IntArray(vertices.size){ -1 }
    distances[from] = 0
    val queue = ArrayDeque<Int>()
    queue.add(from)
    while(queue.size > 0){
        val node = queue.removeFirst()
        val curDist = distances[node]
        vertices[node].edges.filter{ distances[it.to] == -1 }.forEach{
            val delta = it.weight?: 1
            distances[it.to] = curDist + delta
            queue.add(it.to)
        }
    }
    return distances
}
data class Vertex<T : Comparable<T>, E : Comparable<E>>(val data: T? = null) {
    data class Edge<T : Comparable<T>>(val to: Int, val weight: T? = null)

    val edges = mutableListOf<Edge<E>>()

    fun addEdge(to: Int, weight: E?) = when (edges.find { it.to == to }) {
        null -> {
            edges.add(Edge(to, weight))
            true
        }
        else -> false
    }

    fun removeEdge(to: Int): Boolean{
        for ((i, edge) in edges.withIndex()){
            if (edge.to == to){
                edges.removeAt(i)
                return true
            }
        }
        return false
    }
}

class AdjacentListGraph<T : Comparable<T>, E : Comparable<E>>(
    val vertices: MutableList<Vertex<T, E>>
) {
    // T = data of Vertex, E = weight of Edge
    fun getWeight(from: Int, to: Int): E? = vertices[from].edges.find { it.to == to }?.weight
    fun addEdge(from: Int, to: Int, weight: E? = null) = vertices[from].addEdge(to, weight)
    fun removeEdge(from: Int, to: Int) = vertices[from].removeEdge(to)
    fun isAdjacent(from: Int, to: Int) = vertices[from].edges.find { it.to == to } != null
}


fun main(args: Array<String>) {
    fun StringArray(size: Int, init: (Int) -> String = { "\u0000" }): Array<String> {
        return Array<String>(size, init)
    }
    class Scanner(stream: InputStream) {
        private val reader = BufferedInputStream(stream).bufferedReader()
        private var st: StringTokenizer? = null
        fun next(): String {
            while (!(st?.hasMoreTokens() ?: false)) st = StringTokenizer(reader.readLine())
            return st!!.nextToken()
        }
    }
    val sc = Scanner(System.`in`)
    val N = sc.next().toInt()
    val a = IntArray((N-1).toInt())
    val b = IntArray((N-1).toInt())
    for (i in 0 until (N-1).toInt()) {
        a[i] = sc.next().toInt()
        b[i] = sc.next().toInt()
    }
    solve(N, a, b)
}