Problem: You are given a tree consisting of n nodes. You want to write some labels on the tree's edges such that the following conditions hold:

  * Every label is an integer between 0 and n-2 inclusive. 
  * All the written labels are distinct. 
  * The largest value among MEX(u,v) over all pairs of nodes (u,v) is as small as possible. 



Here, MEX(u,v) denotes the smallest non-negative integer that isn't written on any edge on the unique simple path from node u to node v.

Input

The first line contains the integer n (2 ≤ n ≤ 10^5) — the number of nodes in the tree.

Each of the next n-1 lines contains two space-separated integers u and v (1 ≤ u,v ≤ n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.

Output

Output n-1 integers. The i^{th} of them will be the number written on the i^{th} edge (in the input order).

Examples

Input


3
1 2
1 3


Output


0
1


Input


6
1 2
1 3
2 4
2 5
5 6


Output


0
3
2
4
1

Note

The tree from the second sample:

<image>

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import javafx.util.Pair;

public class Solve6 {

    public static void main(String[] args) throws IOException {
        PrintWriter pw = new PrintWriter(System.out);
        new Solve6().solve(pw);
        pw.flush();
        pw.close();
    }

    public void solve(PrintWriter pw) throws IOException {
        FastReader sc = new FastReader();
        int n = sc.nextInt();
        ArrayList<Pair<Integer, Integer>>[] adj = new ArrayList[n + 1];
        for (int i = 1; i <= n; i++) {
            adj[i] = new ArrayList();
        }
        for (int i = 0; i < n - 1; i++) {
            int x = sc.nextInt(), y = sc.nextInt();
            adj[x].add(new Pair(y, i));
            adj[y].add(new Pair(x, i));
        }
        ans = new int[n - 1];
        Arrays.fill(ans, -1);
        timer2 = n - 2;
        dfs(-1, 1, -1, adj);
        for (int i = 0; i < n - 1; i++) {
            pw.println(ans[i]);
        }
    }
    int[] ans;
    int timer, timer2;

    public void dfs(int p, int u, int j, ArrayList<Pair<Integer, Integer>>[] adj) {
        int child = 0;
        for (Pair<Integer, Integer> temp : adj[u]) {
            int v = temp.getKey();
            if (v != p) {
                ++child;
                dfs(u, v, temp.getValue(), adj);
            }
        }
        if (child == 0) {
            ans[j] = timer++;
        } else if (p != -1) {
            ans[j] = timer2--;
        }
    }

    static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
            }
        }

        public String next() {
            if (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            try {
                return br.readLine();
            } catch (Exception e) {
            }
            return null;
        }

        public boolean hasNext() throws IOException {
            if (st != null && st.hasMoreTokens()) {
                return true;
            }
            String s = br.readLine();
            if (s == null || s.isEmpty()) {
                return false;
            }
            st = new StringTokenizer(s);
            return true;
        }
    }
}