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 namespace std::chrono;
long long mod = 1000000007;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
void init() {}
void solve() {
  long long x, y, n, i, j;
  cin >> n;
  vector<pair<long long, long long> > adj(n - 1);
  vector<long long> deg(n + 1, 0);
  for (i = 0; i < n - 1; i++) {
    cin >> x >> y;
    deg[x]++;
    deg[y]++;
    adj[i] = {x, y};
  }
  vector<long long> edge;
  for (i = 0; i < n + 1; i++) {
    if (deg[i] == 1) {
      edge.push_back(i);
    }
  }
  if ((int)edge.size() == 2) {
    for (i = 0; i < n - 1; i++) {
      cout << i << endl;
    }
  } else {
    long long ep = 0, elp = 3;
    for (i = 0; i < n - 1; i++) {
      bool flag = false;
      for (j = 0; j < 3; j++) {
        if (edge[j] == adj[i].first or edge[j] == adj[i].second) {
          flag = true;
        }
      }
      if (flag) {
        cout << ep << endl;
        ep++;
      } else {
        cout << elp << endl;
        elp++;
      }
    }
  }
}
int main() {
  init();
  auto start = high_resolution_clock::now();
  int T = 1;
  while (T--) {
    solve();
  }
  auto stop = high_resolution_clock::now();
  auto duration = duration_cast<milliseconds>(stop - start);
}