Problem: You are given a tree with N vertices 1,2,\ldots,N, and positive integers c_1,c_2,\ldots,c_N. The i-th edge in the tree (1 \leq i \leq N-1) connects Vertex a_i and Vertex b_i.

We will write a positive integer on each vertex in T and calculate our score as follows:

* On each edge, write the smaller of the integers written on the two endpoints.
* Let our score be the sum of the integers written on all the edges.



Find the maximum possible score when we write each of c_1,c_2,\ldots,c_N on one vertex in T, and show one way to achieve it. If an integer occurs multiple times in c_1,c_2,\ldots,c_N, we must use it that number of times.

Constraints

* 1 \leq N \leq 10000
* 1 \leq a_i,b_i \leq N
* 1 \leq c_i \leq 10^5
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 \ldots c_N


Output

Use the following format:


M
d_1 \ldots d_N


where M is the maximum possible score, and d_i is the integer to write on Vertex i. d_1,d_2,\ldots,d_N must be a permutation of c_1,c_2,\ldots,c_N. If there are multiple ways to achieve the maximum score, any of them will be accepted.

Examples

Input

5
1 2
2 3
3 4
4 5
1 2 3 4 5


Output

10
1 2 3 4 5


Input

5
1 2
1 3
1 4
1 5
3141 59 26 53 59


Output

197
59 26 3141 59 53

Solution (in CPP):

Solution:
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<queue>
using namespace std;
const int N=1e5+5;

int l[N],e[2*N],x[2*N];

void pshe(int t,int u,int v){
	x[t]=l[u];l[u]=t;e[t]=v;
}

int c[N],a[N],d[N];

queue<int>q;

int main()
{
	int n,i,j,u,v;
	scanf("%d",&n);
	for(i=1;i<n;i++){
		scanf("%d%d",&u,&v);
		++d[u],++d[v];
		pshe(i<<1,u,v);
		pshe(i<<1|1,v,u);
	}
	for(i=1;i<=n;i++)
		scanf("%d",&c[i]);
	sort(c+1,c+n+1);
	int ans=0;
	for(i=1;i<n;i++)
		ans+=c[i];
	printf("%d\n",ans);
	for(i=1;i<=n;i++)
		if(d[i]==1)
			q.push(i);
	for(j=1;j<=n;j++){
		v=q.front();q.pop();
		--d[v];a[v]=c[j];
		for(i=l[v];i;i=x[i])
			if(d[e[i]]){
				--d[e[i]];
				if(d[e[i]]==1)
					q.push(e[i]);
			}
	}
	for(i=1;i<=n;i++)
		printf("%d ",a[i]);
	return 0;
}