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() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  while (t--) {
    long long n;
    cin >> n;
    vector<pair<long long, long long> > v;
    pair<long long, long long> p;
    map<long long, long long> m;
    for (long long i = 0; i < n - 1; i++) {
      cin >> p.first >> p.second;
      v.push_back(p);
      m[p.first]++;
      m[p.second]++;
    }
    long long x = n - 2, y = 0;
    for (long long i = 0; i < n - 1; i++) {
      if (m[v[i].first] == 1 || m[v[i].second] == 1)
        cout << y++ << '\n';
      else
        cout << x-- << '\n';
    }
  }
  return 0;
}