Problem:
Score : 900 points

Problem Statement

Takahashi has an ability to generate a tree using a permutation (p_1,p_2,...,p_n) of (1,2,...,n), in the following process:

First, prepare Vertex 1, Vertex 2, ..., Vertex N.
For each i=1,2,...,n, perform the following operation:

If p_i = 1, do nothing.

If p_i \neq 1, let j' be the largest j such that p_j < p_i. Span an edge between Vertex i and Vertex j'.

Takahashi is trying to make his favorite tree with this ability.
His favorite tree has n vertices from Vertex 1 through Vertex n, and its i-th edge connects Vertex v_i and w_i.
Determine if he can make a tree isomorphic to his favorite tree by using a proper permutation.
If he can do so, find the lexicographically smallest such permutation.

Notes

For the definition of isomorphism of trees, see wikipedia. Intuitively, two trees are isomorphic when they are the "same" if we disregard the indices of their vertices.

Constraints

2 \leq n \leq 10^5

1 \leq v_i, w_i \leq n

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

n
v_1 w_1
v_2 w_2
:
v_{n-1} w_{n-1}

Output

If there is no permutation that can generate a tree isomorphic to Takahashi's favorite tree, print -1.
If it exists, print the lexicographically smallest such permutation, with spaces in between.

Sample Input 1

6
1 2
1 3
1 4
1 5
5 6

Sample Output 1

1 2 4 5 3 6

If the permutation (1, 2, 4, 5, 3, 6) is used to generate a tree, it looks as follows:

This is isomorphic to the given graph.

Sample Input 2

6
1 2
2 3
3 4
1 5
5 6

Sample Output 2

1 2 3 4 5 6

Sample Input 3

15
1 2
1 3
2 4
2 5
3 6
3 7
4 8
4 9
5 10
5 11
6 12
6 13
7 14
7 15

Sample Output 3

-1

Solution in Haskell (GHC 7.10.3) (judge verdict: Runtime Error)

import Control.Monad
import Data.List
import qualified Data.IntSet as Set
import qualified Data.IntMap as Map
import Debug.Trace

main = do
  n <- readLn
  es <- replicateM (n-1) $ fmap ((\[x,y]->(x,y)) . map read . words) getLine
  case solve es of
    Nothing -> print (-1)
    Just as -> putStrLn (unwords (map show as))

type BoneSet = Set.IntSet
type BoneMap = Map.IntMap [Int]

solve :: [(Int,Int)] -> Maybe [Int]
solve es =
  toPermRep (head ends) bones (restruct bones es)
  where
    (vs,ws) = unzip es

    bones :: Set.IntSet
    bones = Set.fromList . map head . filter ((>1).length) . group . sort $ vs++ws

    ends :: [Int]
    ends = map head . filter((==1).length) . group . sort . concat $ [[v,w]| (v,w)<-es, v`Set.member`bones, w`Set.member`bones]

restruct :: BoneSet -> [(Int,Int)] -> BoneMap
restruct bones es =
  go es Map.empty
  where
    go :: [(Int,Int)] -> Map.IntMap [Int] -> Map.IntMap [Int]
    go []         m = m
    go ((v,w):ds) m = case (v`Set.member`bones, w`Set.member`bones) of
                        (True, False) -> go ds (Map.alter (f w) v m)
                        (False, True) -> go ds (Map.alter (f w) v m)
                        _             -> go ds (Map.alter (f v) w (Map.alter (f w) v m))

    f :: Int -> Maybe [Int] -> Maybe [Int]
    f w Nothing   = Just [w]
    f w (Just ws) = Just (w:ws)

toPermRep :: Int -> BoneSet -> BoneMap -> Maybe [Int]
toPermRep end bones m =
  --traceShow m $ traceShow bones $ traceShow end $
  go end end 1 m [] []
  where
    go cur prev idx m hd tl =
      case Map.lookup cur m of
        Just ws -> let (bs,cs) = partition (`Set.member`bones) ws
                       step = length cs
                   in case filter (/=prev) bs of
                        [b] -> go b cur (idx+step+1) (Map.delete cur m) ([idx+1..idx+step]++hd) (idx:tl)
                        _   -> if Map.null (Map.delete cur m)
                                 then Just ([idx+1..idx+step] ++ hd ++ reverse (idx:tl))
                                 else Nothing
        _       -> Nothing