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;
class Solution {
 private:
  int n;
  vector<pair<int, int> > edges;
  vector<int> deg;

 public:
  Solution() {
    scanf("%d", &n);
    deg = vector<int>(n, 0);
    int u, v;
    for (int i = 1; i < n; i++) {
      scanf("%d %d", &u, &v);
      u--;
      v--;
      edges.push_back({u, v});
      deg[u]++;
      deg[v]++;
    }
  }
  void solve() {
    int l = 0, r = n - 2, u, v;
    for (int i = 0; i < n - 1; i++) {
      u = edges[i].first;
      v = edges[i].second;
      if (deg[u] == 1 || deg[v] == 1)
        printf("%d\n", l++);
      else
        printf("%d\n", r--);
    }
  }
};
int main() {
  Solution *sol = new Solution();
  sol->solve();
  return 0;
}