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
readline = sys.stdin.readline

def parorder(Edge, p):
    N = len(Edge)
    par = [0]*N
    par[p] = -1
    stack = [p]
    order = []
    visited = set([p])
    ast = stack.append
    apo = order.append
    while stack:
        vn = stack.pop()
        apo(vn)
        for vf in Edge[vn]:
            if vf in visited:
                continue
            visited.add(vf)
            par[vf] = vn
            ast(vf)
    return par, order

def getcld(p):
    res = [[] for _ in range(len(p))]
    for i, v in enumerate(p[1:], 1):
        res[v].append(i)
    return res

def dfs(St):
    dist = [0]*N
    stack = St[:]
    used = [False]*N
    for s in St:
        used[s] = True
    while stack:
        vn = stack.pop()
        for vf in Edge[vn]:
            if not used[vf]:
                used[vf] = True
                dist[vf] = 1 + dist[vn]
                stack.append(vf)
    return dist

N = int(readline())
Edge = [[] for _ in range(N)]
for _ in range(N-1):
    a, b = map(int, readline().split())
    a -= 1
    b -= 1
    Edge[a].append(b)
    Edge[b].append(a)

dist0 = dfs([0])
fs = dist0.index(max(dist0))
distfs = dfs([fs])
en = distfs.index(max(distfs))
disten = dfs([en])

Dia = distfs[en]
path = []
for i in range(N):
    if distfs[i] + disten[i] == Dia:
        path.append(i)

if max(dfs(path)) > 1:
    print(-1)
else:
    
    path.sort(key = lambda x: distfs[x])
    
    cnt = 1
    hold = 0
    perm1 = [None]*N
    onpath = set(path)
    idx = 0
    for i in range(Dia+1):
        vn = path[i]
        hold = 0
        for vf in Edge[vn]:
            if vf in onpath:
                continue
            hold += 1
            perm1[idx] = cnt + hold
            idx += 1
        perm1[idx] = cnt
        idx += 1
        cnt = cnt+hold+1
    
    cnt = 1
    hold = 0
    perm2 = [None]*N
    onpath = set(path)
    idx = 0
    for i in range(Dia+1):
        vn = path[Dia-i]
        hold = 0
        for vf in Edge[vn]:
            if vf in onpath:
                continue
            hold += 1
            perm2[idx] = cnt + hold
            idx += 1
        perm2[idx] = cnt
        idx += 1
        cnt = cnt+hold+1
    print(*min(perm1, perm2))