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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cstring>

/* run this program using the console pauser or add your own getch, system("pause") or input loop */

using namespace std;

const int N=100005;

struct edge{
	int v;
	edge *next;
}pool[3*N],*h[N];

int n,top=-1;
int p[N],dep[N],flag[N];
int S,T;
int ans[N],Index,deg[N],dfn[N],_Index;
int ans2[N];
int oscar;

inline void addedge(int u,int v){
	edge *tmp=&pool[++top];
	tmp->v=v;tmp->next=h[u];h[u]=tmp;
}

void dfs(int u,int pre){
	p[u]=pre;
	dep[u]=dep[pre]+1;
	for(edge *tmp=h[u];tmp!=NULL;tmp=tmp->next){
		int v=tmp->v;
		if(v==pre) continue;
		dfs(v,u);
	}
}

void solve(int u,int pre){
	
//	printf("- %d %d\n",u,pre);
	
	dfn[u]=++_Index;
	if(flag[u]==false){
		if(deg[u]>1) oscar=true;
		return ;
	}
	if(u==T){
		ans[++Index]=dfn[u];
		return ;
	}
	int son;
	for(edge *tmp=h[u];tmp!=NULL;tmp=tmp->next){
		int v=tmp->v;
		if(v==pre) continue;
		if(flag[v]==false){
			solve(v,u);
			ans[++Index]=dfn[v];
		}
		else son=v;
	}
	ans[++Index]=dfn[u];
	solve(son,u);
}

void init(){
	int x1,x2;
	scanf("%d",&n);
	for(int i=1;i<n;i++){
		scanf("%d%d",&x1,&x2);
		addedge(x1,x2);
		addedge(x2,x1);
		deg[x1]++;deg[x2]++;
	}
	dfs(1,0);
	for(int i=1;i<=n;i++) if(dep[i]>dep[S]) S=i;
	dfs(S,0);
	for(int i=1;i<=n;i++) if(dep[i]>dep[T]) T=i;
	for(int i=T;i>0;i=p[i]) flag[i]=true;
	solve(S,0);
	if(oscar==true){
		printf("-1\n");
		return ;
	}
	for(int i=1;i<=n;i++) ans2[i]=ans[i];
	_Index=Index=0;
	swap(S,T);
	dfs(S,0);
	solve(S,0);
	/*
	for(int i=1;i<=n;i++) printf("%d ",ans[i]); printf("\n");
	for(int i=1;i<=n;i++) printf("%d ",ans2[i]); printf("\n");
	*/
	for(int i=1;i<=n;i++){
		if(ans[i]<ans2[i]){
			for(int j=1;j<=n;j++) printf("%d ",ans[j]);
			return ;
		}
		if(ans[i]>ans2[i]){
			for(int j=1;j<=n;j++) printf("%d ",ans2[j]);
			return ;
		}
	}
	for(int i=1;i<=n;i++) printf("%d ",ans2[i]);
}

int main(int argc, char** argv) {
	init();
	return 0;
}