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 b[100000];
int main() {
  int n, i, v = 0, s;
  cin >> n;
  s = n - 2;
  int a[n - 1][2];
  for (i = 0; i < n - 1; i++) {
    cin >> a[i][0] >> a[i][1];
    b[a[i][0]]++;
    b[a[i][1]]++;
  }
  for (i = 0; i < n - 1; i++) {
    if (b[a[i][0]] == 1 || b[a[i][1]] == 1)
      cout << v++ << endl;
    else
      cout << s-- << endl;
  }
}