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 n;
  cin >> n;
  vector<int> adj[n + 1];
  int i, j;
  for (i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    adj[u].push_back(i);
    adj[v].push_back(i);
  }
  int out[n + 1];
  memset(out, -1, sizeof(out));
  int q = 0;
  for (i = 1; i <= n; i++) {
    int count = 0;
    if (adj[i].size() > 2) {
      for (j = 0; j < adj[i].size(); j++) {
        out[adj[i][j]] = q;
        q += 1;
      }
      break;
    }
  }
  for (i = 1; i <= n; i++) {
    for (j = 0; j < adj[i].size(); j++) {
      if (out[adj[i][j]] == -1) {
        out[adj[i][j]] = q;
        q += 1;
      }
    }
  }
  for (i = 1; i < n; i++) cout << out[i] << endl;
}