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 n, ans[100005];
vector<pair<int, int> > g[100005];
int main() {
  cin >> n;
  for (long long i = 1; i < n; i++) {
    ans[i] = -1;
    int x, y;
    cin >> x >> y;
    g[x].push_back({y, i});
    g[y].push_back({x, i});
  }
  for (long long i = 1; i <= n; i++) {
    if (g[i].size() > 2) {
      int x = g[i][0].second;
      int y = g[i][1].second;
      int z = g[i][2].second;
      ans[x] = 0;
      ans[y] = 1;
      ans[z] = 2;
      int idx = 3;
      for (long long i = 1; i < n; i++) {
        if (ans[i] == -1) {
          ans[i] = idx;
          idx++;
        }
      }
      for (long long i = 1; i < n; i++) cout << ans[i] << endl;
      return 0;
    }
  }
  for (long long i = 1; i < n; i++) cout << i - 1 << endl;
}