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 fileIO() {}
int n, u, v, numOfEdge[(int)1e5 + 5], ans[(int)1e5 + 5];
vector<pair<int, int>> edge;
void bigBang() {
  cin >> n;
  edge.resize(n + 1);
  for (size_t i = (1); i < (n); ++i) {
    cin >> u >> v;
    edge[i] = {u, v};
    numOfEdge[u]++;
    numOfEdge[v]++;
  }
  memset(ans, -1, sizeof(ans));
  int label = n - 2;
  for (size_t i = (1); i < (n); ++i)
    if (numOfEdge[edge[i].first] > 1 && numOfEdge[edge[i].second] > 1)
      ans[i] = label--;
  for (size_t i = (1); i < (n); ++i)
    if (ans[i] == -1) ans[i] = label--;
  for (size_t i = (1); i < (n); ++i) cout << ans[i] << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(0);
  ;
  fileIO();
  bigBang();
  return 0;
}