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() {
  int n, a, b, sz, j;
  cin >> n;
  vector<int> v[n];
  map<pair<int, int>, int> mp;
  vector<pair<int, int>> vp;
  for (int i = 0; i < n - 1; i++) {
    cin >> a >> b;
    a--;
    b--;
    v[a].push_back(b);
    v[b].push_back(a);
    vp.push_back({a, b});
    mp[{a, b}] = -100;
  }
  sz = 0;
  for (int i = 0; i < n; i++) {
    if (v[i].size() >= 3) {
      sz = v[i].size();
      for (int j = 0; j < v[i].size(); j++) {
        if (mp.find({v[i][j], i}) != mp.end())
          mp[{v[i][j], i}] = j;
        else
          mp[{i, v[i][j]}] = j;
      }
      break;
    }
  }
  j = sz;
  for (auto it = mp.begin(); it != mp.end(); ++it) {
    if (it->second == -100) it->second = j++;
  }
  for (int i = 0; i < vp.size(); i++) {
    pair<int, int> p;
    p = vp[i];
    cout << mp[p] << "\n";
  }
}