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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author maheshwari29
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CEhabAndPathEticMEXs solver = new CEhabAndPathEticMEXs();
        solver.solve(1, in, out);
        out.close();
    }

    static class CEhabAndPathEticMEXs {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int i, j;
            int n = in.ni();
            ArrayList<Integer> arr[] = new ArrayList[n];
            int temp[] = new int[n + 1];
            CEhabAndPathEticMEXs.pair edges[] = new CEhabAndPathEticMEXs.pair[n - 1];
            for (i = 0; i < n - 1; i++) {
                int p = in.ni();
                int q = in.ni();
                temp[p]++;
                temp[q]++;
                edges[i] = new CEhabAndPathEticMEXs.pair(p, q);
            }
            int min = 0, max = n - 2;
            int max_degree = 0;
            for (i = 1; i <= n; i++)
                if (temp[max_degree] < temp[i])
                    max_degree = i;
            for (i = 0; i < n - 1; i++) {
                CEhabAndPathEticMEXs.pair p = edges[i];
                if (p.x == max_degree || p.y == max_degree)
                    out.println(min++);
                else
                    out.println(max--);
            }
        }

        static class pair implements Comparable<CEhabAndPathEticMEXs.pair> {
            int x;
            int y;

            public pair(int x, int y) {
                this.x = x;
                this.y = y;
            }

            public int compareTo(CEhabAndPathEticMEXs.pair arg0) {
                if (x < arg0.x) return -1;
                else if (x == arg0.x) {
                    if (y < arg0.y) return -1;
                    else if (y > arg0.y) return 1;
                    else return 0;
                } else return 1;
            }

            public boolean equals(Object o) {
                if (this == o) return true;
                if (!(o instanceof CEhabAndPathEticMEXs.pair)) return false;
                CEhabAndPathEticMEXs.pair key = (CEhabAndPathEticMEXs.pair) o;
                return x == key.x && y == key.y;
            }

            public int hashCode() {
                int result = x;
                result = 31 * result + y;
                return result;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public 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++];
        }

        public int ni() {
            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;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

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

        public void println(int i) {
            writer.println(i);
        }

    }
}