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_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<int> vis(n, 0);
  vector<int> deg(n, 0);
  vector<pair<int, int>> g;
  int mx = 0;
  for (int i = 0; i < n - 1; ++i) {
    int u, v;
    cin >> u >> v;
    --u;
    --v;
    g.push_back({u, v});
    deg[u]++;
    deg[v]++;
    mx = max(mx, deg[u]);
    mx = max(mx, deg[v]);
  }
  if (mx < 3) {
    for (int i = 0; i < n - 1; ++i) {
      cout << i << endl;
    }
    return 0;
  }
  int id;
  for (int i = 0; i < n; ++i) {
    if (deg[i] > 2) {
      id = i;
      break;
    }
  }
  int ptr = 2;
  int x = n - 2;
  for (int i = 0; i < n - 1; ++i) {
    if ((g[i].first == id || g[i].second == id) && ptr >= 0) {
      cout << ptr << endl;
      ptr--;
    } else {
      cout << x << endl;
      x--;
    }
  }
  return 0;
}