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;
using ii = pair<int, int>;
int main() {
  int n;
  cin >> n;
  vector<vector<ii>> tree(n);
  for (int i = 0; i < n - 1; ++i) {
    int u, v;
    cin >> u >> v;
    --u;
    --v;
    tree[u].push_back({v, i});
    tree[v].push_back({u, i});
  }
  queue<ii> q;
  for (int i = 0; i < n; ++i) {
    if (tree[i].size() == 1) {
      q.push(tree[i][0]);
    }
  }
  vector<int> ans(n - 1, -1);
  int cur_i = 0;
  while (!q.empty()) {
    int u = q.front().first;
    int i = q.front().second;
    q.pop();
    if (ans[i] != -1) {
      continue;
    }
    ans[i] = cur_i++;
    for (const auto& e : tree[i]) {
      q.push(e);
    }
  }
  for (int i = 0; i < n - 1; ++i) {
    cout << ans[i] << endl;
  }
}