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;
const int MOD = 1e9 + 7;
const long long int INF = 1e12;
const int N = 1e5 + 1;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n;
  cin >> n;
  vector<int> adj[n + 1];
  vector<pair<int, int> > edges;
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    edges.push_back(make_pair(min(u, v), max(u, v)));
    adj[u].push_back(v), adj[v].push_back(u);
  }
  int temp = 0;
  map<pair<int, int>, int> mappy;
  for (int v = 1; v <= n; v++) {
    if (adj[v].size() > 2) {
      for (int u : adj[v]) mappy[make_pair(min(u, v), max(u, v))] = temp++;
      break;
    }
  }
  for (pair<int, int> e : edges) {
    pair<int, int> s =
        make_pair(min(e.first, e.second), max(e.first, e.second));
    if (mappy.find(s) != mappy.end()) {
      cout << mappy[s] << "\n";
    } else {
      cout << temp++ << "\n";
    }
  }
  return 0;
}