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: Accepted)

import Control.Monad
import Control.Monad.ST
import Control.Applicative
import Data.List
import Data.Array
import Data.Array.IO
import Data.Array.ST
import Data.Maybe
import Data.Bits
import Data.Ord
import Data.Ratio
import Data.Int
import Data.Char
import qualified Data.ByteString.Char8 as BS
import qualified Data.Set as Set
import Text.Printf
import Debug.Trace
import Numeric

modifyArray arr i f = readArray arr i >>= \x -> writeArray arr i (f x)

listToTuple2 [a,b] = (a,b)
listToTuple3 [a,b,c] = (a,b,c)
listToTuple4 [a,b,c,d] = (a,b,c,d)

getWords = getLine >>= return . words

readIntBS = fst . fromJust . BS.readInt

for = flip map

type Graph = Array Int [Int]

buildGraph :: (Int,Int) -> [(Int,Int)] -> Graph
buildGraph bound dat = runST $ do
  graph <- newArray bound [] :: ST s (STArray s Int [Int])
  forM_ dat $ \(s,e) -> do
    modifyArray graph s (e:)
    modifyArray graph e (s:)
  freeze graph



main :: IO ()
main = do
  n <- readLn :: IO Int
  graph <- buildGraph (1,n) . map (listToTuple2 . map readIntBS . BS.words) . BS.lines <$> BS.getContents :: IO Graph

  let
    dfs :: Int -> Int -> Graph -> Maybe [Int]
    dfs cur par tree
      | cur == n = Just [n]
      | otherwise = if next == [] then Nothing else Just (cur : head next)
        where
          next = catMaybes $ map (\i -> dfs i cur tree) (delete par $ tree!cur)

    (Just chain) = dfs 1 0 graph

    count :: Int -> Int -> Graph -> Int
    count cur par tree = 1 + (sum $ [count i cur tree | i <- tree!cur, i /= par])

    branch [] _ = []
    branch (x:xs) prev = 1 + sum [count i x graph | i <- graph!x, i /= prev, i /= next] : branch xs x
      where next = if null xs then 0 else head xs
    
    (fennec, snuke) = splitAt (ceiling $ (length chain) % 2) $ branch chain 0

  putStrLn $ if sum fennec > sum snuke then "Fennec" else "Snuke"