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

input=sys.stdin.readline
sys.setrecursionlimit(2*10**5)

n=int(input())
edge=[[] for i in range(n)]
for i in range(n-1):
    v,w=map(int,input().split())
    edge[v-1].append(w-1)
    edge[w-1].append(v-1)

if n==2:
    exit(print(1,2))

leafcnt=[0]*n
for v in range(n):
    for nv in edge[v]:
        if len(edge[nv])==1:
            leafcnt[v]+=1

used=[False]*n
line=[]
def line_check(v):
    used[v]=True
    line.append(leafcnt[v])
    flag=False
    for nv in edge[v]:
        if not used[nv] and len(edge[nv])!=1:
            if not flag:
                line_check(nv)
                flag=True
            else:
                return False
    return True

for v in range(n):
    if not used[v] and len(edge[v])-leafcnt[v]<=1 and len(edge[v])!=1:
        if not line:
            check=line_check(v)
            if not check:
                exit(print(-1))
        else:
            exit(print(-1))


line_rev=line[::-1]
res=min(line,line_rev)
res=[0]+res+[0]
res[1]-=1
res[-2]-=1

ans=[]
L=1
for val in res:
    R=L+val
    for i in range(L+1,R+1):
        ans.append(i)
    ans.append(L)
    L=R+1

print(*ans)
