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() {
  int n;
  cin >> n;
  vector<vector<int>> g(n + 1);
  vector<int> ans(n - 1, -1);
  for (int i = 0; i < n - 1; ++i) {
    int x1, x2;
    cin >> x1 >> x2;
    g[x1].push_back(i);
    g[x2].push_back(i);
  }
  int i = 0;
  while (i <= n && g[i].size() < 3) ++i;
  if (i <= n)
    for (int j = 0; j < 3; ++j) ans[g[i][j]] = j;
  int count = n - 1;
  for (auto& c : ans)
    if (c == -1) c = --count;
  for (auto c : ans) cout << c << endl;
  return 0;
}