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;
list<int> adjList[100005];
int mxdeg = -1;
int mv = -1;
int ans[100005];
int sz[100005];
int main() {
  int(n);
  scanf("%d", &(n));
  vector<pair<int, int> > v;
  for (int i = 0; i < n - 1; i++) {
    int(a), (b);
    scanf("%d %d", &(a), &(b));
    adjList[a].push_back(b);
    adjList[b].push_back(a);
    v.push_back({a, b});
    sz[a]++;
    sz[b]++;
    if (sz[a] > mxdeg) {
      mxdeg = sz[a];
      mv = a;
    }
    if (sz[b] > mxdeg) {
      mxdeg = sz[b];
      mv = b;
    }
  }
  int ctr = 1;
  for (int i = 0; i < n - 1; i++) {
    if (v[i].first == mv || v[i].second == mv) ans[i] = ctr, ctr++;
  }
  for (int i = 0; i < n - 1; i++) {
    if (!ans[i]) ans[i] = ctr, ctr++;
  }
  for (int i = 0; i < n - 1; i++) {
    cout << ans[i] - 1 << "\n";
  }
  return 0;
}