Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

10
1 2 3 4 5

If we write 1,2,3,4,5 on Vertex 1,2,3,4,5, respectively, the integers written on the four edges will be 1,2,3,4, for the score of 10. This is the maximum possible score.

Sample Input 2

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

Sample Output 2

197
59 26 3141 59 53

c_1,c_2,\ldots,c_N may not be pairwise distinct.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;

public class Main {
	private static boolean[] vis;
	private static long[] dist;
	public static void merge(int arr[], int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
	 public static void sort(int arr[], int l, int r) 
	    { 
	        if (l < r) 
	        { 
	            // Find the middle point 
	            int m = (l+r)/2; 
	  
	            // Sort first and second halves 
	            sort(arr, l, m); 
	            sort(arr , m+1, r); 
	  
	            // Merge the sorted halves 
	            merge(arr, l, m, r); 
	        } 
	    } 
	 private static int gcd(int n, int l) {
	        if (l == 0)
	            return n;
	        return gcd(l, n % l);
	    }
//	 public static void dfs(ArrayList<Integer>[] gr,int v,int[] ans,HashMap<Integer,HashMap<Integer,Integer>> map)
//	    {
//	         vis[v]=true;
//	         ArrayList<Integer> arr=gr[v];
//	         for(int i=0;i<arr.size();i++)
//	         {
//	             if(!vis[arr.get(i)])
//	             {  
//	            	 
//	            	 dfs(gr,arr.get(i));
//	             }
//	         }
//	    }
	 private static class Pairs implements Comparable<Pairs>{
	        String v;int i;int j;
	        public Pairs(String a,int b,int c){
	            v=a;
	            i=b;
	            j=c;
	        }
	        @Override
	        public int compareTo(Pairs arg0) {
	            {
	            	if(!this.v.equals(arg0.v))
	            		return this.v.compareTo(arg0.v);
	            	else
	            		return arg0.i-this.i;
	            }
	        }
	    }
	 private static class Pair implements Comparable<Pair>{
	        int v,i;Pair j;
	        public Pair(int a,int b){
	            v=a;
	            i=b;
	        }
	        public Pair(int a,Pair b)
	        {
	            v=a;
	            j=b;
	        }
	        @Override
	        public int compareTo(Pair arg0) {
	            {
	            	return this.v-arg0.v;
	            }
	        }
	    }
	 public static long mmi(long a, long m) 
	    { 
	        long m0 = m; 
	        long y = 0, x = 1; 
	      
	        if (m == 1) 
	          return 0; 
	      
	        while (a > 1) 
	        { 
	            // q is quotient 
	            long q = a / m; 
	            long t = m; 
	      
	            // m is remainder now, process same as 
	            // Euclid's algo 
	            m = a % m; a = t; 
	            t = y; 
	      
	            // Update y and x 
	            y = x - q * y; 
	            x = t; 
	        } 
	      
	        // Make x positive 
	        if (x < 0) 
	           x += m0; 
	      
	        return x; 
	    }
	public static void main(String[] args) throws Exception
	{
		Scanner sc=new Scanner(System.in);
	    int n=sc.nextInt();
	    ArrayList<Integer>[] g=new ArrayList[n+1];
	    for(int i=01;i<=n;i++)	g[i]=new ArrayList<>();
	    for(int i=0;i<n-1;i++)
	    {
	    	int a=sc.nextInt();int b=sc.nextInt();
	    	g[a].add(b);g[b].add(a);
	    }
	    int[] c=new int[n];
	    for(int i=0;i<n;i++)	c[i]=sc.nextInt();
	    int[] ans=new int[n+1];
	    sort(c,0,n-1);
	    boolean visited[] = new boolean[n+1]; 
	    
        // Create a queue for BFS 
        LinkedList<Integer> queue = new LinkedList<Integer>(); 
  
        // Mark the current node as visited and enqueue it 
        visited[1]=true; 
        queue.add(1); 
        int k=n-1;
        while (queue.size() != 0) 
        { 
            // Dequeue a vertex from queue and print it 
            int s = queue.poll(); 
            ans[s]=c[k];k--;
            // Get all adjacent vertices of the dequeued vertex s 
            // If a adjacent has not been visited, then mark it 
            // visited and enqueue it 
            for(int i=0;i<g[s].size();i++)
            {
            	if(!visited[g[s].get(i)])
            	{
            		visited[g[s].get(i)]=true;
            		queue.add(g[s].get(i));
            	}
            }
        }
        for(int i=1;i<=n;i++)	System.out.print(ans[i]+" ");
	}
}