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 Go (1.6) (judge verdict: Accepted)

package main

import (
    "bufio"
    "os"
    "fmt"
    "strconv"
    "container/heap"
)

const INF = 1000000000000000

/*********** PriorityQueue ***********/
type PriorityQueue struct {
    arr []interface{}
    comps []CompFunc
}
/*
p < q ... -1
p == q ... 0
p > q ...  1
*/
type CompFunc func(p, q interface{}) int

func NewPriorityQueue() *PriorityQueue {
    return new(PriorityQueue)
}

func (pq PriorityQueue) Len() int {
    return len(pq.arr)
}

func (pq PriorityQueue) Swap(i, j int) {
    pq.arr[i], pq.arr[j] = pq.arr[j], pq.arr[i]
}

func (pq PriorityQueue) Less(i, j int) bool{
    for _, comp := range pq.comps {
        result := comp(pq.arr[i], pq.arr[j])
        switch result {
            case -1: return true
            case 1:  return false
            case 0:  continue
        }
    }
    return true
}

func (pq *PriorityQueue) Push(x interface{}) {
    pq.arr = append(pq.arr, x)
}

func (pq *PriorityQueue) Pop() interface{} {
    n := pq.Len()
    item := pq.arr[n - 1]
    pq.arr = pq.arr[:n - 1]
    return item
}

func (pq *PriorityQueue) IsEmpty() bool {
    return pq.Len() == 0
}



/* for dijkstra */
/* type Edge */
type Edge struct {
    to int
    cost int
}

/* type State */
type State struct {
    score int
    node int
}

/* type Graph */
type Graph struct {
    starts []State
    edges [][]Edge
    size int
    comps []CompFunc
    defaultScore int
}

func dijkstra(graph *Graph) []int {
    score := make([]int, graph.size)
    for i := 0; i < graph.size; i++ {
        score[i] = graph.defaultScore
    }
    que := new(PriorityQueue)
    que.comps = graph.comps
    for _, start := range graph.starts {
        score[start.node] = start.score
        heap.Push(que, start)
    }
    for !que.IsEmpty() {
        state := heap.Pop(que).(State)
        for _, edge := range graph.edges[state.node] {
            newScore := state.score + edge.cost
            if score[edge.to] > newScore {
                score[edge.to] = newScore
                heap.Push(que, State{score: newScore, node: edge.to})
            }
        }
    }
    return score
}

/* input */
var sc = bufio.NewScanner(os.Stdin)

func readInt() int {
    sc.Scan()
    n, _ := strconv.Atoi(sc.Text())
    return n
}

func main() {
    sc.Split(bufio.ScanWords)
    n := readInt()
    var edges [][]Edge
    for i := 0; i < n; i++ {
        edges = append(edges, make([]Edge, 0))
    }
    for i := 0; i < n - 1; i++ {
        a, b := readInt() - 1, readInt() - 1
        edges[a] = append(edges[a], Edge{to:b, cost:1})
        edges[b] = append(edges[b], Edge{to:a, cost:1})
    }
    comp := func(p, q interface{}) int {
        if p.(State).score < q.(State).score {
            return -1
        } else if p.(State).score == q.(State).score {
            return 0
        } else {
            return 1
        }
        return 0
    }
    comps := make([]CompFunc, 0)
    comps = append(comps, comp)
    starts1 := make([]State, 0)
    starts2 := make([]State, 0)
    starts1 = append(starts1, State{score:0, node:0})
    starts2 = append(starts2, State{score:0, node:n - 1})

    graph1 := new(Graph)
    graph1.edges = edges
    graph1.starts = starts1
    graph1.size = n
    graph1.comps = comps
    graph1.defaultScore = INF

    graph2 := new(Graph)
    graph2.edges = edges
    graph2.starts = starts2
    graph2.size = n
    graph2.comps = comps
    graph2.defaultScore = INF

    dist1 := dijkstra(graph1)
    dist2 := dijkstra(graph2)
    black := 0
    for i := 0; i < n; i++ {
        if dist1[i] <= dist2[i] {
            black++
        }
    }
    white := n - black
    if white >= black {
        fmt.Println("Snuke")
    } else {
        fmt.Println("Fennec")
    }
}