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.math.*;
import java.util.*;

/**
 *
 * @author Saju
 *
 */

public class Main {

    private static int dx[] = { 1, 0, -1, 0 };
    private static int dy[] = { 0, -1, 0, 1 };

    private static final long INF = (long) Math.pow(10, 16);
    private static final int INT_INF = Integer.MAX_VALUE;
    private static final long NEG_INF = Long.MIN_VALUE;
    private static final int NEG_INT_INF = Integer.MIN_VALUE;
    private static final double EPSILON = 1e-10;

    private static final long MAX = (long) 1e12;
    
    private static final long MOD = 1000000007;

    private static final int MAXN = 300005;
    private static final int MAXA = 1000007;
    private static final int MAXLOG = 22;
    private static final double PI = Math.acos(-1);
    
	public static void main(String[] args) throws IOException {

		InputReader in = new InputReader(System.in);
//		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

//         InputReader in = new InputReader(new FileInputStream("src/test.in"));
//         PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("src/test.out")));

		
		
/*



*/		
		
		int n = in.nextInt();
		List<Edge> adj[] = new ArrayList[n];
		for(int i = 0; i < n; i++) {
			adj[i] = new ArrayList<>();
		}
		
		int three = -1;
		
		for(int i = 0; i < n - 1; i++) {
			int u = in.nextInt() - 1;
			int v = in.nextInt() - 1;
			adj[u].add(new Edge(u, v, i));
			adj[v].add(new Edge(v, u, i));
			if(three == -1 && adj[u].size() >= 3) {
				three = u;
			}
			if(three == -1 && adj[v].size() >= 3) {
				three = v;
			}
		}
		
		
		int[] ans = new int[n];
		Arrays.fill(ans, -1);
		int cnt = 0;
		
		int st = 0;
		
		if(three != -1) {
			st = three;
			for(Edge e : adj[st]) {
				if(cnt == 3) {
					break;
				}
				ans[e.id] = cnt++;
			}
		}
		
		boolean visited[] = new boolean[n];
		
		Queue<Integer> queue = new LinkedList<>();
		queue.add(st);
		visited[st] = true;
		while(!queue.isEmpty()) {
			int u = queue.remove();
			
			for(Edge e : adj[u]) {
				if(!visited[e.v]) {
					visited[e.v] = true;
					queue.add(e.v);
					if(ans[e.id] == -1) {
						ans[e.id] = cnt++;
					}
				}
			}
		}
		
		for(int i = 0; i < n - 1; i++) {
			out.println(ans[i]);
		}			
		
		
		
		
		
		in.close();
		out.flush();
		out.close();
		System.exit(0);
	}
	
	private static class Edge{
		int u;
		int v;
		int id;
		int label;
		Edge(int u, int v, int id){
			this.u = u;
			this.v = v;
			this.id = id;
		}
	}

	/*
	 * return the number of elements in list that are less than or equal to the val
	 */
	private static long upperBound(List<Long> list, long val) {
		int start = 0;
		int len = list.size();
		int end = len - 1;
		int mid = 0;

		while (true) {
			if (start > end) {
				break;
			}
			mid = (start + end) / 2;
			long v = list.get(mid);
			if (v == val) {
				start = mid;
				while(start < end) {
					mid = (start + end) / 2;
					if(list.get(mid) == val) {
						if(mid + 1 < len && list.get(mid + 1) == val) {
							start = mid + 1;
						}
						else {
							return mid + 1;
						}
					}
					else {
						end = mid - 1;
					}
				}
				return start + 1;
			}
			if (v > val) {
				end = mid - 1;
			} else {
				start = mid + 1;
			}
		}
		if (list.get(mid) < val) {
			return mid + 1;
		}
		return mid;
	}


	private static boolean isPalindrome(String str) {
		StringBuilder sb = new StringBuilder();
		sb.append(str);
		String str1 = sb.reverse().toString();
		return str.equals(str1);
	}

	private static String getBinaryStr(long n, int j) {
		String str = Long.toBinaryString(n);
		int k = str.length();
		for (int i = 1; i <= j - k; i++) {
			str = "0" + str;
		}

		return str;
	}
	
	private static long modInverse(long r) {
		return bigMod(r, MOD - 2, MOD);
	}
	
	private static long bigMod(long n, long k, long m) {

        long ans = 1;
        while (k > 0) {
            if ((k & 1) == 1) {
                ans = (ans * n) % m;
            }
            n = (n * n) % m;
            k >>= 1;
        }
        return ans;
    }
    
	private static long ceil(long n, long x) {
		long div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
	}
	
    private static int ceil(int n, int x) {
        int div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
    }

    
    private static int abs(int x) {
        if (x < 0) {
            return -x;
        }
        return x;
    }
    
    private static double abs(double x) {
        if (x < 0) {
            return -x;
        }
        return x;
    }

    private static long abs(long x) {
        if(x < 0) {
            return -x;
        }
        return x;
    }
    
    private static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    private static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }

    private static int gcd(int a, int b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }
    
    private static long gcd(long a, long b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    private static int log(long x, int base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    private static int log(long x, long base) {
        return (int) (Math.log(x) / Math.log(base));
    }
    
    private static long min(long a, long b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static int min(int a, int b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static long max(long a, long b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static int max(int a, int b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());

                }
            } catch (IOException e) {
                return null;
            }
            return tokenizer.nextToken();
        }

        public String nextLine() {
            String line = null;
            try {
                tokenizer = null;
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

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

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

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

        public boolean hasNext() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());
                }
            } catch (Exception e) {
                return false;
            }
            return true;
        }
        
        public int[] nextIntArr(int n) {
        	int arr[] = new int[n];
    		for(int i = 0; i < n; i++) {
    			arr[i] = nextInt();
    		}
    		return arr;
        }
        
        public long[] nextLongArr(int n) {
        	long arr[] = new long[n];
    		for(int i = 0; i < n; i++) {
    			arr[i] = nextLong();
    		}
    		return arr;
        }
        
        public int[] nextIntArr1(int n) {
        	int arr[] = new int[n + 1];
    		for(int i = 1; i <= n; i++) {
    			arr[i] = nextInt();
    		}
    		return arr;
        }
        
        public long[] nextLongArr1(int n) {
        	long arr[] = new long[n + 1];
    		for(int i = 1; i <= n; i++) {
    			arr[i] = nextLong();
    		}
    		return arr;
        }
       
        public void close() {
        	try {
        		if(reader != null) {
        			reader.close();
        		}
        	}
        	catch(Exception e) {
        		
        	}
        	
        	
        }
    }

}