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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Problem628C {
	public static void main(String[] args) throws Exception {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(reader.readLine());
		int[] u = new int[n - 1];
		int[] v = new int[n - 1];
		int[] degreeCount = new int[n];
		for (int i = 0; i < n - 1; i++) {
			StringTokenizer aT = new StringTokenizer(reader.readLine());
			u[i] = Integer.parseInt(aT.nextToken()) - 1;
			v[i] = Integer.parseInt(aT.nextToken()) - 1;
			degreeCount[u[i]]++;
			degreeCount[v[i]]++;
		}
		int maxNode = 0;
		int maxDegree = Integer.MIN_VALUE;
		for (int i = 0; i < n; i++) {
			if (degreeCount[i] > maxDegree) {
				maxDegree = degreeCount[i];
				maxNode = i;
			}
		}
		Set<Integer> maxEdges = new TreeSet<Integer>();
		for (int i = 0; i < u.length; i++) {
			if (u[i] == maxNode || v[i] == maxNode) {
				maxEdges.add(i);
			}
		}
		//System.out.println(maxNode + " " + maxDegree + " " + maxEdges);

		// 0 through maxDegree are reserved
		int a = 0;
		int current = maxDegree;
		for (int i = 0; i < n - 1; i++) {
			if (maxEdges.contains(i)) {
				System.out.println(a++);
			} else {
				System.out.println(current++);
			}
		}

		reader.close();
	}
}