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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import qualified Data.ByteString.Char8 as B
import Data.Maybe
import Data.List
import Data.Array.IArray
import Control.Monad

data Player = Fennec | Snuke deriving (Eq,Show)

type Vertex = Int
type Edge = (Vertex,Vertex)
type Graph = Array Vertex [Vertex]

readEdge :: B.ByteString -> [Edge]
readEdge = (\[a,b] -> [(a,b),(b,a)]) . map (fst . fromJust . B.readInt) . B.words

groupFrom :: [Edge] -> [[Edge]]
groupFrom = groupBy (\(v1,_) (v2,_) -> v1 == v2)

main :: IO ()
main = do
 n <- readLn
 es <- sort . concatMap readEdge . B.lines <$> B.getContents
 let g = array (1,n) $ map (\ps -> ((fst.head) ps, map snd ps)) (groupFrom es)
 print (versus n g)

versus :: Vertex -> Graph -> Player
versus n g = if nf > ns then Fennec else Snuke
 where
  dmz = dfsDMZ g [] 0 1 n
  border = take 2 (drop (div (length dmz) 2 - 1) dmz) 
  nf = dfsDomain g 0 1 (head border)
  ns = dfsDomain g 0 n (last border)

dfsDMZ :: Graph -> [Vertex] -> Vertex -> Vertex -> Vertex -> [Vertex]
dfsDMZ g acc vp v vg
 | v == vg = v:acc
 | null next = mzero
 | otherwise = msum $ map (\vn -> dfsDMZ g (v:acc) v vn vg) next
 where next = delete vp (g!v)

dfsDomain :: Graph -> Vertex -> Vertex -> Vertex -> Int
dfsDomain g vp v vg
 | v == vg = 0
 | otherwise = sum $ do
    vn <- g!v
    guard (vn /= vp)
    return (1 + dfsDomain g v vn vg)