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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int a, b, i, n;
  int edges[int(2e5 + 1)][2], weights[int(2e5 + 1)], freq[int(2e5 + 1)];
  cin >> n;
  for (i = 1; i <= n; i++) freq[i] = 0;
  for (i = 0; i < n; i++) {
    weights[i] = -1;
    cin >> edges[i][0] >> edges[i][1];
    freq[edges[i][0]]++;
    freq[edges[i][1]]++;
  }
  int maxindex = 1, k = 0;
  for (i = 1; i <= n; i++)
    if (freq[i] > freq[maxindex]) maxindex = i;
  for (i = 0; i < n; i++)
    if (edges[i][0] == maxindex or edges[i][1] == maxindex) weights[i] = k++;
  for (i = 0; i < n; i++)
    if (weights[i] == -1) weights[i] = k++;
  for (i = 0; i < n - 1; i++) cout << weights[i] << endl;
  return 0;
}