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;
void solve() {}
int main() {
  int n;
  cin >> n;
  vector<int> v(n, 0);
  vector<int> x(n, 0);
  vector<int> y(n, 0);
  for (int i = 0; i < n - 1; i++) {
    cin >> x[i] >> y[i];
    v[x[i] - 1]++;
    v[y[i] - 1]++;
  }
  int q = 0;
  for (int i = 0; i < n; i++) {
    if (v[i] >= 3) {
      q = i + 1;
    }
  }
  if (q == 0) {
    for (int i = 0; i < n - 1; i++) {
      cout << i << endl;
    }
  } else {
    int j = 3;
    int jj = 0;
    for (int i = 0; i < n - 1; i++) {
      if (jj >= 3 || (y[i] != q && x[i] != q)) {
        cout << j << endl;
        j++;
      } else {
        cout << jj << endl;
        jj++;
      }
    }
  }
  return 0;
}