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 n, l[100009];
vector<int> v[100009];
pair<int, int> p[100009];
int main() {
  cin.tie(0);
  cout.tie(0);
  ios::sync_with_stdio(0);
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (int i = 0, x, y; i < n - 1; i++) {
    cin >> x >> y;
    x--;
    y--;
    v[x].push_back(y);
    v[y].push_back(x);
    p[i] = {x, y};
  }
  for (int i = 0; i < n; i++) {
    if (v[i].size() == 1) l[i] = 1;
  }
  for (int i = 0, x, y, j = 0, k = n - 2; i < n - 1; i++) {
    x = p[i].first;
    y = p[i].second;
    if (l[x] || l[y]) {
      cout << j << "\n";
      j++;
    } else {
      cout << k << "\n";
      k--;
    }
  }
}