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 + 5;
int values[N] = {};
vector<pair<int, int>> g[N];
bool cmp(vector<pair<int, int>> a, vector<pair<int, int>> b) {
  return a.size() > b.size();
}
void solve(int n) {
  int m = 0;
  for (int i = 0; i < n; ++i) {
    for (auto& p : g[i]) {
      if (values[p.second] == -1) {
        values[p.second] = m;
        m++;
        if (m > n - 2) return;
      }
    }
  }
}
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n - 1; ++i) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    g[u].emplace_back(make_pair(v, i));
    g[v].emplace_back(make_pair(u, i));
  }
  fill(values, values + n, -1);
  sort(g, g + n, cmp);
  solve(n);
  for (int i = 0; i < n - 1; ++i) {
    cout << values[i] << endl;
  }
}