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 wejsce[100010][2];
int wyniki[100010];
vector<pair<int, int>> tab[100010];
int main() {
  int n, i, a, b;
  scanf("%d", &n);
  for (i = 1; i < n; i++) {
    scanf("%d%d", &a, &b);
    tab[a].push_back({b, i});
    tab[b].push_back({a, i});
  }
  int czy = 0;
  for (i = 1; i <= n; i++) {
    if (tab[i].size() > 2) {
      for (int j = 0; j < 3; j++) {
        wyniki[tab[i][j].second] = j + 1;
      }
      czy = 1;
      i = n + 1;
    }
  }
  int j = 3;
  if (czy == 0) j = 0;
  for (i = 1; i < n; i++) {
    if (wyniki[i] == 0) {
      printf("%d\n", j);
      j++;
    } else
      printf("%d\n", wyniki[i] - 1);
  }
}