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;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  while (t--) {
    long long n;
    cin >> n;
    vector<long long> adj[n + 1];
    vector<pair<long long, long long> > p;
    map<pair<long long, long long>, long long> vis;
    vector<long long> cnt(n + 1, 0);
    for (long long i = 0; i < n - 1; i++) {
      long long x, y;
      cin >> x >> y;
      cnt[x]++;
      cnt[y]++;
      adj[x].push_back(y);
      adj[y].push_back(x);
      p.push_back({x, y});
    }
    long long mx = 0;
    for (long long i = 1; i <= n; i++) {
      if (cnt[i] > 2) {
        vis[{i, adj[i][0]}] = 0;
        vis[{i, adj[i][1]}] = 1;
        vis[{i, adj[i][2]}] = 2;
        mx = 3;
        break;
      }
    }
    for (long long i = 0; i < n - 1; i++) {
      if (vis.count(p[i]))
        cout << vis[p[i]] << '\n';
      else if (vis.count({p[i].second, p[i].first}))
        cout << vis[{p[i].second, p[i].first}] << '\n';
      else
        cout << mx << '\n', mx++;
    }
  }
}