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 N = 1e5 + 100;
vector<vector<pair<int, int>>> aj(N);
vector<int> ans(N, -1);
int main(int argc, char *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  for (int i = 0; i < n - 1; ++i) {
    int u, v;
    cin >> u >> v;
    aj[u].emplace_back(i, v);
    aj[v].emplace_back(i, u);
  }
  for (int v = 1; v <= n; ++v) {
    if (aj[v].size() > 2) {
      int k = 0;
      for (auto p : aj[v]) {
        ans[p.first] = k++;
      }
      for (int i = 0; i < n - 1; ++i) {
        if (ans[i] != -1) {
          cout << ans[i] << endl;
        } else {
          cout << k++ << endl;
        }
      }
      return 0;
    }
  }
  for (int i = 0; i < n - 1; ++i) {
    cout << i << endl;
  }
  return 0;
}