Problem: This problem is split into two tasks. In this task, you are required to find the minimum possible answer. In the task Village (Maximum) you are required to find the maximum possible answer. Each task is worth 50 points.

There are N houses in a certain village. A single villager lives in each of the houses. The houses are connected by roads. Each road connects two houses and is exactly 1 kilometer long. From each house it is possible to reach any other using one or several consecutive roads. In total there are N-1 roads in the village.

One day all villagers decided to move to different houses — that is, after moving each house should again have a single villager living in it, but no villager should be living in the same house as before. We would like to know the smallest possible total length in kilometers of the shortest paths between the old and the new houses for all villagers.

<image>

Example village with seven houses 

For example, if there are seven houses connected by roads as shown on the figure, the smallest total length is 8 km (this can be achieved by moving 1 → 6, 2 → 4, 3 → 1, 4 → 2, 5 → 7, 6 → 3, 7 → 5).

Write a program that finds the smallest total length of the shortest paths in kilometers and an example assignment of the new houses to the villagers.

Input

The first line contains an integer N (1 < N ≤ 10^5). Houses are numbered by consecutive integers 1, 2, …, N.

Then N-1 lines follow that describe the roads. Each line contains two integers a and b (1 ≤ a, b ≤ N, a ≠ b) denoting that there is a road connecting houses a and b.

Output

In the first line output the smallest total length of the shortest paths in kilometers.

In the second line describe one valid assignment of the new houses with the smallest total length: N space-separated distinct integers v_1, v_2, …, v_N. For each i, v_i is the house number where the villager from the house i should move (v_i ≠ i). If there are several valid assignments, output any of those.

Scoring

Subtasks: 

  1. (6 points) N ≤ 10 
  2. (19 points) N ≤ 1 000 
  3. (25 points) No further constraints 

Examples

Input


4
1 2
2 3
3 4


Output


4
2 1 4 3


Input


7
4 2
5 7
3 4
6 3
1 3
4 5


Output


8
3 4 6 2 7 1 5

Solution (in JAVA):

Solution:
/*
ID: davidzh8
PROG: subset
LANG: JAVA
 */

import java.io.*;
import java.util.*;
import java.lang.*;

public class villagemin {

    static long startTime = System.nanoTime();
    static ArrayList<Integer>[] adj;
    static int[] pos;
    public static void solve() throws Exception {
        boolean debug = (true);
        FastScanner sc = new FastScanner("villagemin.in", debug);
        FastWriter pw = new FastWriter("villagemin.out", debug);
        int N= sc.ni();
        adj= new ArrayList[N];
        pos= new int[N];
        for (int i = 0; i < N; i++) {
            pos[i]=i;
        }
        for(int i=0; i<N; i++){
            adj[i]= new ArrayList<>();
        }
        for (int i = 0; i < N-1; i++) {
            int a= sc.ni()-1;
            int b= sc.ni()-1;
            adj[a].add(b);
            adj[b].add(a);
        }
        dfs(0,-1);
        System.out.println(res);
        for (int i = 0; i < N; i++) {
            System.out.print(pos[i]+1+" ");
        }


        long endTime = System.nanoTime();
        //System.out.println("Execution Time: " + (endTime - startTime) / 1e9 + " s");
        pw.close();
    }
    static int res=0;
    static void dfs(int cur, int par){
        for(int next: adj[cur] ){
            if(next==par) continue;
            dfs(next, cur);
            if(pos[next]==next) {
                res += 2;
                int temp = pos[cur];
                pos[cur] = pos[next];
                pos[next] = temp;
            }
        }
        if(cur==0 && pos[cur]==0){
            int next= adj[0].get(0);
            res += 2;
            int temp = pos[cur];
            pos[cur] = pos[next];
            pos[next] = temp;
        }

    }


    static class Pair implements Comparable<Pair> {
        int a;
        int b;

        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair obj) {
            if (obj.a == a) {
                return b - obj.b;
            } else return a - obj.a;
        }
    }


    static class djset {
        int N;
        int[] parent;

        // Creates a disjoint set of size n (0, 1, ..., n-1)
        public djset(int n) {
            parent = new int[n];
            N = n;
            for (int i = 0; i < n; i++)
                parent[i] = i;
        }

        public int find(int v) {

            // I am the club president!!! (root of the tree)
            if (parent[v] == v) return v;

            // Find my parent's root.
            int res = find(parent[v]);

            // Attach me directly to the root of my tree.
            parent[v] = res;
            return res;
        }

        public boolean union(int v1, int v2) {

            // Find respective roots.
            int rootv1 = find(v1);
            int rootv2 = find(v2);

            // No union done, v1, v2 already together.
            if (rootv1 == rootv2) return false;

            // Attach tree of v2 to tree of v1.
            parent[rootv2] = rootv1;
            return true;
        }


    }

    static class FastScanner {
        InputStream dis;
        byte[] buffer = new byte[1 << 17];
        int pointer = 0;

        public FastScanner(String fileName, boolean debug) throws Exception {
            if (debug) dis = System.in;
            else dis = new FileInputStream(fileName);
        }

        int ni() throws Exception {
            int ret = 0;

            byte b;
            do {
                b = nextByte();
            } while (b <= ' ');
            boolean negative = false;
            if (b == '-') {
                negative = true;
                b = nextByte();
            }
            while (b >= '0' && b <= '9') {
                ret = 10 * ret + b - '0';
                b = nextByte();
            }

            return (negative) ? -ret : ret;
        }

        long nl() throws Exception {
            long ret = 0;

            byte b;
            do {
                b = nextByte();
            } while (b <= ' ');
            boolean negative = false;
            if (b == '-') {
                negative = true;
                b = nextByte();
            }
            while (b >= '0' && b <= '9') {
                ret = 10 * ret + b - '0';
                b = nextByte();
            }

            return (negative) ? -ret : ret;
        }

        byte nextByte() throws Exception {
            if (pointer == buffer.length) {
                dis.read(buffer, 0, buffer.length);
                pointer = 0;
            }
            return buffer[pointer++];
        }

        String next() throws Exception {
            StringBuffer ret = new StringBuffer();

            byte b;
            do {
                b = nextByte();
            } while (b <= ' ');
            while (b > ' ') {
                ret.appendCodePoint(b);
                b = nextByte();
            }

            return ret.toString();
        }
    }

    static class FastWriter {
        public PrintWriter pw;

        public FastWriter(String name, boolean debug) throws IOException {
            if (debug) {
                pw = new PrintWriter(System.out);
            } else {
                pw = new PrintWriter(new BufferedWriter(new FileWriter(new File(name))));
            }
        }

        public void println(Object text) {
            pw.println(text);
        }

        public void print(Object text) {
            pw.print(text);
        }

        public void close() {
            pw.close();
        }

        public void flush() {
            pw.flush();
        }
    }

    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, () -> {
            try {
                solve();
            } catch (Exception e) {
                e.printStackTrace();
            }
        }, "", 1 << 28);
        thread.start();
        thread.join();
    }

}