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;
using ll = long long;
using pii = pair<int, int>;
void solve() {
  int n;
  scanf("%d", &n);
  vector<vector<pii> > g(n);
  int u, v;
  vector<int> label(n - 1, -1);
  for (int i = 1; i < n; i++) {
    scanf("%d %d", &u, &v);
    u--, v--;
    g[u].push_back(make_pair(v, i - 1));
    g[v].push_back(make_pair(u, i - 1));
  }
  int num = 0;
  for (int u = 0; u < n; u++) {
    if (g[u].size() >= 3) {
      label[g[u][0].second] = 0;
      label[g[u][1].second] = 1;
      label[g[u][2].second] = 2;
      num = 3;
      break;
    }
  }
  for (int i = 0; i < n - 1; i++) {
    if (label[i] == -1) {
      label[i] = num++;
    }
  }
  for (int x : label) {
    printf("%d ", x);
  }
  printf("\n");
}
int main() {
  int T = 1;
  while (T--) {
    solve();
  }
  return 0;
}