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.*;
import java.util.*;
 
/**
 * A simple template for competitive programming problems.
 */
public class Solution {
    //final InputReader in = new InputReader("input.txt");
    final InputReader in = new InputReader(System.in);
 
    final PrintWriter out = new PrintWriter(System.out);
 
    void solve() {
        int n = in.nextInt();
        Node[] nodes = new Node[n+1];
        Edge[] edges = new Edge[n-1];
        for(int i=0; i<=n; i++) { nodes[i] = new Node();}
        for(int i=0; i<n-1; i++) {
            int u = in.nextInt();
            int v = in.nextInt();
 
            edges[i] = new Edge();
            edges[i].u = u; edges[i].v = v; edges[i].i = i;
 
            nodes[u].es.add(edges[i]);
            nodes[v].es.add(edges[i]);
        }
 
        int count = 0;
 
        for(int i=1; i<=n; i++) {
            int s = nodes[i].es.size();
            if(s>2) {
                for(Edge e : nodes[i].es) {
                    e.l = count++;
                }
                break;
            }
        }
 
        for(Edge e : edges) {
            if(e.l != -1)
                continue;
            e.l = count++;
        }
 
        for(int i=0; i<n-1; i++) {
            out.println(edges[i].l);
        }
    }
 
    class Node {
        List<Edge> es = new ArrayList<>();
    }
 
    class Edge {
        int u; int v; int i;
        int l = -1;
    }
    public static void main(String[] args) throws FileNotFoundException {
        Solution s = new Solution();
        Long t1 = System.currentTimeMillis();
        s.solve();
        System.err.println(System.currentTimeMillis() - t1 + " ms");
        s.out.close();
    }
 
    public Solution() throws FileNotFoundException {
    }
 
    private static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
 
        InputReader(InputStream stream) {
            this.stream = stream;
        }
 
        InputReader(String fileName) {
            InputStream stream = null;
            try {
                stream = new FileInputStream(fileName);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            this.stream = stream;
        }
 
        int[] nextArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextInt();
            return arr;
        }
 
        int[][] nextMatrix(int n, int m) {
            int[][] matrix = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    matrix[i][j] = nextInt();
            return matrix;
        }
 
        String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        double nextDouble() {
            return Double.parseDouble(nextString());
        }
 
        private int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
 
}