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.

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.

Examples

Input

6
1 2
1 3
1 4
1 5
5 6


Output

1 2 4 5 3 6


Input

6
1 2
2 3
3 4
1 5
5 6


Output

1 2 3 4 5 6


Input

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


Output

-1
import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline

N = int(input())
VW = [[int(x)-1 for x in input().split()] for _ in range(N-1)]

"""
直径に次数1の頂点が生えている
"""

graph = [[] for _ in range(N)]
deg = [0] * N
for v,w in VW:
    graph[v].append(w)
    graph[w].append(v)
    deg[v] += 1
    deg[w] += 1

def dijkstra(start):
    INF = 10**10
    dist = [INF] * N
    q = [(start,0)]
    while q:
        qq = []
        for v,d in q:
            dist[v] = d
            for w in graph[v]:
                if dist[w] == INF:
                    qq.append((w,d+1))
        q = qq
    return dist

dist = dijkstra(0)
v = dist.index(max(dist))
dist = dijkstra(v)
w = dist.index(max(dist))
diag = v,w

def create_perm(start):
    arr = []
    v = start
    parent = None
    next_p = 1
    while True:
        n = 0
        next_v = None
        for w in graph[v]:
            if w == parent:
                continue
            if next_v is None or deg[next_v] < deg[w]:
                next_v = w
            if deg[w] == 1:
                n += 1
        if next_v is None:
            return arr + [next_p]
        if deg[next_v] == 1:
            n -= 1
        arr += list(range(next_p+1,next_p+n+1))
        arr.append(next_p)
        next_p += n+1
        parent = v
        v = next_v

P = create_perm(diag[1])

Q = create_perm(diag[0])

if len(P) != N:
    answer = -1
else:
    if P > Q:
        P = Q
    answer = ' '.join(map(str,P))
print(answer)

