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;
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n;
  cin >> n;
  vector<int> v[n];
  int a = -1;
  for (int i = 0; i < n - 1; ++i) {
    int x, y;
    cin >> x >> y;
    if (a != -1) continue;
    --x, --y;
    v[x].push_back(i);
    v[y].push_back(i);
    if (v[x].size() > 2) a = x;
    if (v[y].size() > 2) a = y;
  }
  if (a == -1) {
    for (int i = 0; i < n - 1; ++i) cout << i << '\n';
    return 0;
  }
  int num = 3;
  for (int i = 0; i < n - 1; ++i) {
    if (i == v[a][0])
      cout << "0\n";
    else if (i == v[a][1])
      cout << "1\n";
    else if (i == v[a][2])
      cout << "2\n";
    else
      cout << num++ << '\n';
  }
}