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, u[maxn], v[maxn], w[maxn];
int ind[maxn];
int main(void) {
  scanf("%d", &n);
  for (int i = 1; i < n; i++)
    scanf("%d%d", u + i, v + i), ind[u[i]]++, ind[v[i]]++, w[i] = -1;
  int m = 0;
  for (int i = 1; i <= n; i++)
    if (ind[i] >= 3) {
      for (int j = 1; j < n; j++)
        if (u[j] == i || v[j] == i) {
          w[j] = m++;
          if (m == 3) break;
        }
      break;
    }
  for (int i = 1; i < n; i++)
    if (w[i] == -1) w[i] = m++;
  for (int i = 1; i < n; i++) printf("%d\n", w[i]);
  return 0;
}