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.*;
import java.text.*;

public class C1325 {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int[] cnt = new int[n];
		int[] u = new int[n - 1];
		int[] v = new int[n - 1];
		for (int i = 0; i < n - 1; i++) {
			u[i] = sc.nextInt() - 1;
			v[i] = sc.nextInt() - 1;
			cnt[u[i]]++;
			cnt[v[i]]++;
		}
		HashSet<Integer> leaves = new HashSet<Integer>();
		for (int i = 0; i < n; i++) {
			if (cnt[i] == 1)
				leaves.add(i);
		}
		int[] ans = new int[n - 1];
		Arrays.fill(ans, -1);
		int k = 0;
		for (int i = 0; i < n - 1; i++) {
			if (leaves.contains(u[i]) || leaves.contains(v[i])) {
				ans[i] = k++;
			}
		}
		for (int i = 0; i < n - 1; i++) {
			if (ans[i] == -1)
				ans[i] = k++;
		}
		for (int x : ans)
			pw.println(x);
		pw.close();

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < arr.length; i++)
				arr[i] = nextInt();
			return arr;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}
}