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>
struct info {
  int x, index;
  info(int x, int index) : x(x), index(index) {}
};
std::vector<info> graph[100010];
int result[100010];
int main(void) {
  int n;
  scanf("%d", &n);
  for (int i = 1; i < n; i++) {
    int u, v;
    scanf("%d %d", &u, &v);
    graph[u].push_back(info(v, i));
    graph[v].push_back(info(u, i));
    result[i] = -1;
  }
  if (n == 2) {
    printf("0\n");
    return 0;
  }
  int cnt = 0;
  for (int i = 1; i <= n; i++) {
    if (graph[i].size() == 1) {
      result[graph[i][0].index] = cnt++;
    }
  }
  for (int i = 1; i < n; i++) {
    if (result[i] == -1)
      printf("%d\n", cnt++);
    else
      printf("%d\n", result[i]);
  }
}