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 long long mod = 1e9 + 7;
const int N = 1e5 + 20;
int n, ans[N], num = -1;
vector<pair<int, int> > to[N];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = (1); i <= (n - 1); i++) {
    int u, v;
    cin >> u >> v;
    to[u].push_back(make_pair(v, i));
    to[v].push_back(make_pair(u, i));
  }
  memset(ans, -1, sizeof(ans));
  int flag = -1;
  for (int i = (1); i <= (n - 1); i++) {
    if (int(to[i].size()) > 2) flag = i;
  }
  if (flag != -1) {
    for (auto t : to[flag]) {
      ans[t.second] = ++num;
    }
  }
  for (int i = (1); i <= (n - 1); i++) {
    if (ans[i] == -1)
      cout << ++num;
    else
      cout << ans[i];
    cout << '\n';
  }
  return 0;
}