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, x, y;
  cin >> n;
  vector<int> adj[n + 1], deg(n + 1, 0);
  vector<pair<int, int>> input;
  for (int i = 0; i < n - 1; i++) {
    cin >> x >> y;
    input.push_back(make_pair(x, y));
    adj[x].push_back(y);
    adj[y].push_back(x);
    deg[x]++;
    deg[y]++;
  }
  vector<pair<int, int>> s;
  for (int i = 1; i <= n; i++) {
    s.push_back(make_pair(deg[i], i));
  }
  sort(s.begin(), s.end());
  int number = 0;
  map<pair<int, int>, int> m;
  for (auto x : s) {
    int degree = x.first;
    int vertex = x.second;
    for (int k : adj[vertex]) {
      pair<int, int> temp = {k, vertex};
      pair<int, int> revr = {vertex, k};
      if (m.find(temp) == m.end()) {
        m[temp] = number;
        m[revr] = number;
        number++;
      }
    }
  }
  for (auto x : input) {
    pair<int, int> temp = {x.first, x.second};
    cout << m[temp] << "\n";
  }
}