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;
const int N = 3e5 + 10;
const int inf = 1e9;
const int mo = 998244353;
vector<int> a[N];
int ans[N];
int main() {
  int n;
  cin >> n;
  for (auto i = (1); i <= (n - 1); ++i) ans[i] = -1;
  for (auto i = (1); i <= (n - 1); ++i) {
    int u, v;
    cin >> u >> v;
    a[u].push_back(i);
    a[v].push_back(i);
  }
  bool flag = 0;
  for (auto i = (1); i <= (n); ++i) {
    if (a[i].size() >= 3) {
      for (auto j = (1); j <= (3); ++j) {
        ans[a[i][j - 1]] = j - 1;
      }
      flag = 1;
      break;
    }
  }
  int now = 3;
  if (!flag) now = 0;
  for (auto i = (1); i <= (n - 1); ++i) {
    if (ans[i] == -1)
      cout << now++;
    else
      cout << ans[i];
    cout << endl;
  }
  return 0;
}