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 N = 1e5 + 7;
map<long long, long long> ans;
vector<long long> g[N];
map<pair<long long, long long>, long long> d;
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long n;
  cin >> n;
  for (long long i = 0; i < n - 1; ++i) {
    long long u, v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
    d[make_pair(u, v)] = d[make_pair(v, u)] = i;
  }
  long long mx = 1;
  for (long long i = 1; i <= n; ++i) {
    if (g[i].size() > g[mx].size()) {
      mx = i;
    }
  }
  long long ptr = 0;
  for (long long i = 0; i < min(3ll, (long long)g[mx].size()); ++i) {
    long long v = g[mx][i];
    ans[d[make_pair(mx, v)]] = ptr++;
  }
  for (long long i = 0; i < n - 1; ++i) {
    if (ans.find(i) != ans.end()) {
      cout << ans[i] << '\n';
    } else {
      cout << ptr++ << '\n';
    }
  }
}