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 maxn = 1e5 + 5;
int n, a[maxn], b[maxn], du[maxn], cnt = 0, prime;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n - 1; i++) {
    scanf("%d %d", &a[i], &b[i]);
    du[a[i]]++, du[b[i]]++;
  }
  int s = n - 2;
  for (int i = 1; i <= n - 1; i++) {
    if (a[i] == prime || b[i] == prime) {
      printf("%d\n", cnt++);
    } else if (((du[a[i]] > 2 || du[b[i]] > 2)) && prime == 0) {
      printf("%d\n", cnt++);
      if (du[a[i]] > 2) {
        prime = a[i];
      } else {
        prime = b[i];
      }
    } else {
      printf("%d\n", s--);
    }
  }
  return 0;
}