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() {
  long long n, i, j, x, y, edge[100001];
  vector<long long> v[100001];
  map<pair<long long, long long>, long long> mp;
  cin >> n;
  memset(edge, -1, sizeof(edge));
  for (i = 0; i < n - 1; i++) {
    cin >> x >> y;
    mp[{x, y}] = i;
    v[x].push_back(y);
    v[y].push_back(x);
  }
  for (i = 1; i <= n; i++)
    if (v[i].size() > 2) break;
  if (i > n) {
    for (i = 0; i < n - 1; i++) cout << i << "\n";
    return 0;
  }
  for (j = 0; j < 3; j++) {
    if (mp.find({v[i][j], i}) != mp.end()) {
      edge[mp[{v[i][j], i}]] = j;
    } else
      edge[mp[{i, v[i][j]}]] = j;
  }
  x = 3;
  for (i = 0; i < n - 1; i++) {
    if (edge[i] == -1) {
      cout << x << "\n";
      x++;
    } else
      cout << edge[i] << "\n";
  }
  return 0;
}