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;
string str;
struct hash_pair {
  template <class T1, class T2>
  size_t operator()(const pair<T1, T2>& p) const {
    auto hash1 = hash<T1>{}(p.first);
    auto hash2 = hash<T2>{}(p.second);
    return hash1 ^ hash2;
  }
};
void solve() {
  int m, n, a, b, c;
  cin >> n;
  vector<int> vec[n + 1];
  map<pair<int, int>, int> mp;
  vector<pair<int, int> > edges;
  for (int i = 0; i < (int)n - 1; i++) {
    cin >> a >> b;
    vec[a].push_back(b);
    vec[b].push_back(a);
    edges.push_back({min(a, b), max(a, b)});
  }
  c = 0;
  for (int i = 0; i < (int)n; i++) {
    if (vec[i].size() > 2) {
      a = i;
      b = vec[i][0];
      mp[{min(a, b), max(a, b)}] = 0;
      b = vec[i][1];
      mp[{min(a, b), max(a, b)}] = 1;
      b = vec[i][2];
      mp[{min(a, b), max(a, b)}] = 2;
      c = 3;
      break;
    }
  }
  for (int i = 0; i < (int)n - 1; i++) {
    if (mp.find(edges[i]) == mp.end()) {
      mp[edges[i]] = c++;
    }
  }
  for (int i = 0; i < (int)n - 1; i++) {
    cout << mp[edges[i]] << endl;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  int tc = 1;
  while (tc--) {
    solve();
  }
  return 0;
}