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;
void solve() {
  int n;
  cin >> n;
  vector<pair<int, int> > edges(n - 1);
  vector<int> deg(n + 1, 0);
  int root = -1;
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    edges[i] = {u, v};
    deg[u]++, deg[v]++;
    if (deg[u] > 2 && root == -1) root = u;
    if (deg[v] > 2 && root == -1) root = v;
  }
  if (root == -1)
    for (int i = 0; i < n - 1; i++) cout << i << "\n";
  else {
    unordered_set<int> w;
    int rootEdgeWeight = 0;
    for (int i = 3; i < n - 1; i++) w.insert(i);
    for (const auto &p : edges) {
      int u = p.first, v = p.second;
      if ((u == root || v == root) && rootEdgeWeight < 3) {
        cout << rootEdgeWeight++ << "\n";
      } else {
        cout << *w.begin() << "\n";
        w.erase(w.begin());
      }
    }
  }
}
int main() {
  int t = 1;
  while (t--) {
    solve();
  }
}