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;
vector<int> adj[200006];
int n, m;
int color[200006];
void solve() {
  cin >> n;
  int k = -1;
  int color[n];
  memset(color, -1, sizeof color);
  for (int i = 0; i < n - 1; i++) {
    int x, y;
    cin >> x >> y;
    x--, y--;
    adj[x].push_back(i);
    adj[y].push_back(i);
    if (adj[x].size() >= 3) {
      k = x;
    }
    if (adj[y].size() >= 3) {
      k = y;
    }
  }
  int g = 0;
  if (k != -1) {
    for (int i = 0; i < 3; i++) {
      color[adj[k][i]] = g++;
    }
  }
  for (int i = 0; i < n - 1; i++) {
    if (color[i] == -1) color[i] = g++;
    cout << color[i] << endl;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  solve();
}