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 <bits/stdc++.h>

using namespace std;
using nagai = long long;
#define sz(x) int((x).size())

const int N=100100;
vector<int>g[N];
int n;
int c[N];
int ptr;
int ans[N];
void d(int u,int p=-1){
	ans[u]=c[ptr--];
	for(int v:g[u])
		if(v!=p)
			d(v,u);
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin>>n;
	for(int i=0;i<n-1;++i){
		 int a,b;
		 cin>>a>>b;
		 --a,--b;
		 g[a].push_back(b);
		 g[b].push_back(a);
	}
	ptr=n-1;
	for(int i=0;i<n;++i)
		cin>>c[i];
	sort(c,c+n);
	int ans=accumulate(c,c+n-1,0);
	cout<<ans<<'\n';
	d(0);
	for(int i=0;i<n;++i){
		cout<<::ans[i]<<' ';
	}
	cout<<'\n';
	return 0;
}