#include <cstdio>
#include <cstring>
#include <algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
#define rep(i,a) for(int i=lst[a];i;i=nxt[i])
using namespace std;

int read() {
	char ch;
	for(ch=getchar();ch<'0'||ch>'9';ch=getchar());
	int x=ch-'0';
	for(ch=getchar();ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
	return x;
}

const int N=1e5+5;

int t[N<<1],nxt[N<<1],lst[N],l;
void add(int x,int y) {t[++l]=y;nxt[l]=lst[x];lst[x]=l;}

int n,r,tot,mx,fa[N],rk[N],p[N],k[N],an[N];

void get_far(int x,int y,int d) {
	if (d>mx) mx=d,r=x;
	rep(i,x) if (t[i]!=y) get_far(t[i],x,d+1);
}

void dfs(int x,int y) {
	fa[x]=y;
	rep(i,x) if (t[i]!=y) dfs(t[i],x);
}

int main() {
	n=read();
	fo(i,1,n-1) {
		int x=read(),y=read();
		add(x,y);add(y,x);
	}
	mx=r=0;get_far(1,0,0);int u=r;
	mx=r=0;get_far(u,0,0);int v=r;
	dfs(u,0);
	for(int x=v;x;x=fa[x]) p[++tot]=x,rk[x]=tot;
	fo(i,1,n) {
		if (!rk[i]&&!rk[fa[i]]) {puts("-1");return 0;}
		if (!rk[i]) k[rk[fa[i]]]++; 
	}
	bool rev=0;
	for(int i=1,j=tot;i<=tot;i++,j--) {
		if (k[i]>k[j]) {rev=1;break;}
		if (k[i]<k[j]) {rev=0;break;} 
	}
	if (rev) fo(i,1,tot/2) swap(k[i],k[tot-i+1]);
	int m=0;
	fo(i,1,tot) {
		fo(j,m+1,m+k[i]) an[j]=j+1;an[m+k[i]+1]=m+1;
		m+=k[i]+1;
	}
	fo(i,1,n) printf("%d ",an[i]);
	return 0;
}
### Prompt

Your task is to create a Cpp solution to the following problem:

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

### Response

```cpp
#include <cstdio>
#include <cstring>
#include <algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
#define rep(i,a) for(int i=lst[a];i;i=nxt[i])
using namespace std;

int read() {
	char ch;
	for(ch=getchar();ch<'0'||ch>'9';ch=getchar());
	int x=ch-'0';
	for(ch=getchar();ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
	return x;
}

const int N=1e5+5;

int t[N<<1],nxt[N<<1],lst[N],l;
void add(int x,int y) {t[++l]=y;nxt[l]=lst[x];lst[x]=l;}

int n,r,tot,mx,fa[N],rk[N],p[N],k[N],an[N];

void get_far(int x,int y,int d) {
	if (d>mx) mx=d,r=x;
	rep(i,x) if (t[i]!=y) get_far(t[i],x,d+1);
}

void dfs(int x,int y) {
	fa[x]=y;
	rep(i,x) if (t[i]!=y) dfs(t[i],x);
}

int main() {
	n=read();
	fo(i,1,n-1) {
		int x=read(),y=read();
		add(x,y);add(y,x);
	}
	mx=r=0;get_far(1,0,0);int u=r;
	mx=r=0;get_far(u,0,0);int v=r;
	dfs(u,0);
	for(int x=v;x;x=fa[x]) p[++tot]=x,rk[x]=tot;
	fo(i,1,n) {
		if (!rk[i]&&!rk[fa[i]]) {puts("-1");return 0;}
		if (!rk[i]) k[rk[fa[i]]]++; 
	}
	bool rev=0;
	for(int i=1,j=tot;i<=tot;i++,j--) {
		if (k[i]>k[j]) {rev=1;break;}
		if (k[i]<k[j]) {rev=0;break;} 
	}
	if (rev) fo(i,1,tot/2) swap(k[i],k[tot-i+1]);
	int m=0;
	fo(i,1,tot) {
		fo(j,m+1,m+k[i]) an[j]=j+1;an[m+k[i]+1]=m+1;
		m+=k[i]+1;
	}
	fo(i,1,n) printf("%d ",an[i]);
	return 0;
}
```