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
#include <cstdio>
using namespace std;
const int N=100005;
int n,x,y,z,head[N],sum,s,t,maxx;
int step[N],next[N][2],cnt[N],p;
struct edge
{	int to,next;}a[N<<1];
int read()
{	char x=getchar();
	while(x<48||x>57) x=getchar();
	int ans=0;
	while(x>=48&&x<=57)
	{	ans=(ans<<1)+(ans<<3)+(x^48);
		x=getchar();
	}
	return ans;
}
void insert(int x,int y)
{	sum++;a[sum].to=y;a[sum].next=head[x];head[x]=sum;}
void find(int num,int fa)
{	step[num]=step[fa]+1;
	if(step[num]>maxx){maxx=step[num];s=num;}
	int x;
	for(int i=head[num];i;i=a[i].next)
	{	x=a[i].to;
		if(x!=fa) find(x,num);
	}
}
bool judge(int num,int fa)
{	next[num][0]=fa;
	int x;
	for(int i=head[num];i;i=a[i].next)
	{	x=a[i].to;
		if(x==fa) continue;
		if(judge(x,num)) return true;
		cnt[num]++;
		if(cnt[x])
		{	if(next[num][1]) return true;
			next[num][1]=x;
		}
	}
	if(cnt[num]&&!next[num][1]) t=num;
	return false;
}
int main()
{	n=read();
	for(int i=1;i<n;i++)
	{	x=read();y=read();
		insert(x,y);insert(y,x);
	}
	find(1,0);
	if(judge(s,0)){printf("-1\n");return 0;}
	s=next[s][1];x=s;y=t;
	p=1;next[s][0]=0;
	while(x!=y&&next[x][0]!=y)
	{	if(cnt[x]<cnt[y]) break;
		if(cnt[x]>cnt[y])
		{	z=s;s=t;t=z;p=0;break;}
		x=next[x][1];y=next[y][0];
	}
	printf("1 ");x=y=2;
	while(s)
	{	for(cnt[s]--;cnt[s];cnt[s]--)
		printf("%d ",++x);
		printf("%d ",y);
		x++;y=x;
		s=next[s][p];
	}
	printf("%d\n",x);
	return 0;
}