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;
void solve(int n) {
  int cnt = n;
  vector<int> adj[n + 1];
  vector<int> deg(n + 1);
  pair<int, int> arr[n - 1];
  int i = 0;
  while (--cnt) {
    int x1, x2;
    cin >> x1 >> x2;
    deg[x1]++;
    deg[x2]++;
    adj[x1].push_back(x2);
    adj[x2].push_back(x1);
    arr[i].first = x1;
    arr[i].second = x2;
    i++;
  }
  int node = -1;
  for (int i = 1; i <= n; i++) {
    if (deg[i] >= 3) {
      node = i;
      break;
    }
  }
  int weight = n - 2;
  if (node == -1) {
    for (int i = 0; i <= n - 2; i++) {
      cout << weight << "\n";
      weight--;
    }
    return;
  }
  int cnter = deg[node] - 1;
  weight = cnter + 1;
  for (int i = 0; i < n - 1; i++) {
    if (arr[i].first == node or arr[i].second == node) {
      cout << cnter << "\n";
      cnter--;
    } else {
      cout << weight << "\n";
      weight++;
    }
  }
}
int main() {
  int n;
  cin >> n;
  solve(n);
}