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;
  int u[n], v[n];
  vector<int> adj[n + 1];
  for (int i = 1; i <= n - 1; i++) {
    int x, y;
    cin >> x >> y;
    u[i] = x;
    v[i] = y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  int ma = 0;
  for (int i = 1; i <= n; i++) {
    int y = adj[i].size();
    ma = max(ma, y);
  }
  if (ma <= 2) {
    for (int i = 1; i < n; i++) cout << i - 1 << endl;
  } else {
    int h;
    for (int i = 1; i <= n; i++) {
      if (adj[i].size() > 2) {
        h = i;
        break;
      }
    }
    int g = n - 2;
    int d = 0;
    for (int i = 1; i <= n - 1; i++) {
      if (u[i] == h || v[i] == h) {
        cout << d << endl;
        d++;
      } else {
        cout << g << endl;
        g--;
      }
    }
  }
  return 0;
}