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;
const int mxN = 1e5;
int n, eu[mxN], ev[mxN], ans[mxN];
vector<int> adj[mxN];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 1; i < n; ++i) {
    cin >> eu[i] >> ev[i], --eu[i], --ev[i];
    adj[eu[i]].push_back(i);
    adj[ev[i]].push_back(i);
  }
  for (int i = 0; i < n; ++i) {
    if (adj[i].size() <= 2) continue;
    memset(ans, -1, 4 * n);
    for (int j = 0; j < 3; ++j) ans[adj[i][j]] = j;
    for (int i = 1, j = 3; i < n; ++i) {
      if (ans[i] < 0) ans[i] = j++;
      cout << ans[i] << "\n";
    }
    return 0;
  }
  for (int i = 1; i < n; ++i) cout << i - 1 << "\n";
}