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 JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;
// import java.awt.Point;
 
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
 
    // static int mod = 1_000_000_007;
    int mod = 998244353;
    // long inf = Long.MAX_VALUE/2;
    int inf = Integer.MAX_VALUE/2;

    ArrayList<Integer>[] edge;

    void solve(){
        int n = ni();

        edge = new ArrayList[n];
        for(int i = 0; i < n; i++){
            edge[i] = new ArrayList<>();
        }

        int[] e = new int[n];
        for(int i = 0; i < n-1; i++){
            int s = ni()-1;
            int t = ni()-1;
            e[s]++;
            e[t]++;
            edge[s].add(t);
            edge[t].add(s);
        }
        int[] v = new int[n];
        for(int i = 0; i < n; i++){
            v[i] = ni();
        }
        Arrays.sort(v);

        SegmentTree seg = new SegmentTree(n);
        for(int i = 0; i < n; i++){
            seg.update(i,e[i],i);
        }

        int[] map = new int[n];
        int idx = 0;
        for(int i = 0; i < n; i++){
            int[] tmp = seg.query(0,n);
            map[tmp[1]] = v[idx++];
            seg.update(tmp[1],inf,tmp[1]);
            for(int j : edge[tmp[1]]){
                int[] tmp2 = seg.query(j,j+1);
                seg.update(tmp2[1],tmp2[0]-1,tmp2[1]);
            }
        }

        int ans = 0;
        for(int i = 0; i < n-1; i++){
            ans += v[i];
        }
        out.println(ans);
        for(int i = 0; i < n; i++){
            out.print(map[i]+" ");
        }

    }

    class SegmentTree {
        int n;
        int[][] seg;
        SegmentTree(int n) {
            this.n = Integer.highestOneBit(n) << 1;
            this.seg = new int[this.n<<1][2];
            for(int i=0;i<(this.n<<1);++i){
                seg[i][0] = inf;
                seg[i][1] = -1;
            }
        }
        int[] comb(int[] ans1, int[] ans2){
            if(ans1[0]<=ans2[0]){
                return new int[]{ans1[0], ans1[1]};
            }
            return new int[]{ans2[0], ans2[1]};
        }
        void update(int x, int value, int id) {
            x += n - 1;
            this.seg[x][0] = value;
            this.seg[x][1] = id;
            while (x > 0) {
                x = (x - 1) / 2;
                this.seg[x] = comb(this.seg[2 * x + 1], this.seg[2 * x + 2]);
            }
        }
        int[] query(int a,int b,int l,int r,int k){
            if(a<=l&&r<=b) return seg[k];
            if(b<=l||r<=a) return new int[]{inf, -1};
            int[] ans1=query(a,b,l,(l+r)/2,2*k+1);
            int[] ans2=query(a,b,(l+r)/2,r,2*k+2);
            return comb(ans1, ans2);
        }
        int[] query(int l, int r) {
            return query(l,r,0,n,0);
        }
    }

    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b) && b != ' ')){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
 
}