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 int64_t INF = 1e18;
int32_t main() {
  ios_base::sync_with_stdio(false);
  int64_t n;
  cin >> n;
  vector<int64_t> ans(n - 1, -1);
  vector<vector<int64_t> > deg(n);
  for (int64_t i = 0; i < n - 1; i++) {
    int64_t a, b;
    cin >> a >> b;
    a--;
    b--;
    deg[a].push_back(i);
    deg[b].push_back(i);
  }
  int64_t p = -1;
  for (int64_t i = 0; i < n; i++) {
    if (deg[i].size() > 2) p = i;
  }
  if (p == -1) {
    for (int64_t i = 0; i < n - 1; i++) cout << i << endl;
    return 0;
  }
  for (int64_t i = 0; i < 3; i++) ans[deg[p][i]] = i;
  int64_t cnt = 3;
  for (int64_t i = 0; i < n - 1; i++)
    if (ans[i] == -1) ans[i] = cnt++;
  for (int64_t i = 0; i < n - 1; i++) cout << ans[i] << endl;
  return 0;
}