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

public class _1325C {
    static int[] MODS = {1000000007, 998244353, 1000000009};
    static int MOD = MODS[0];

    public static void main(String[] args) {
        sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int n = sc.nextInt();
        int[][] edges = new int[n - 1][2];
        ArrayList<Integer>[] adj = new ArrayList[n+1];
        for (int i = 0; i < adj.length; i++) {
            adj[i] = new ArrayList<>();
        }
        for (int i = 0; i < n - 1; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            adj[a].add(b);
            adj[b].add(a);
            edges[i][0] = a;
            edges[i][1] = b;
        }
        if (n == 2) {
            out.println(0);
        } else if (n == 3) {
            out.println(0);
            out.println(1);
        } else {
            int[] ans = new int[n - 1];
            Arrays.fill(ans, -1);
            ArrayList<Integer> leaves = new ArrayList<>();
            for (int i = 1; i <= n; i++) {
                if (adj[i].size() == 1) {
                    leaves.add(i);
                }
            }
            if (leaves.size() == 2) {
                int first = leaves.get(0);
                int second = leaves.get(1);
                for (int i = 0; i < n - 1; i++) {
                    if (edges[i][0] == first || edges[i][1] == first) {
                        ans[i] = 0;
                    }
                    if (edges[i][0] == second || edges[i][1] == second) {
                        ans[i] = 1;
                    }
                }
                int current = 2;
                for (int i = 0; i < n - 1; i++) {
                    if (ans[i] == -1) {
                        ans[i] = current;
                        current++;
                    }
                }
            } else {
                int first = leaves.get(0);
                int second = leaves.get(1);
                int third = leaves.get(2);
                for (int i = 0; i < n - 1; i++) {
                    if (edges[i][0] == first || edges[i][1] == first) {
                        ans[i] = 0;
                    }
                    if (edges[i][0] == second || edges[i][1] == second) {
                        ans[i] = 1;
                    }
                    if (edges[i][0] == third || edges[i][1] == third) {
                        ans[i] = 2;
                    }
                }
                int current = 3;
                for (int i = 0; i < n - 1; i++) {
                    if (ans[i] == -1) {
                        ans[i] = current;
                        current++;
                    }
                }
            }
            for (int i = 0; i < n - 1; i++) {
                out.println(ans[i]);
            }
        }
        out.close();
    }

    public static int[] sort(int[] arr) {
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 0; i < arr.length; i++) {
            list.add(arr[i]);
        }
        Collections.sort(list);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = list.get(i);
        }
        return arr;
    }

    public static void scan(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            arr[i] = sc.nextInt();
        }
    }

    public static MyScanner sc;
    public static PrintWriter out;

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}