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;
pair<int, int> edges[maxn];
int deg[maxn], ans[maxn];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    deg[u]++, deg[v]++;
    edges[i] = make_pair(u, v);
  }
  int p = -1;
  for (int i = 1; i <= n; i++)
    if (deg[i] >= 3) p = i;
  if (p == -1) {
    for (int i = 0; i < n - 1; i++) cout << i << '\n';
    return 0;
  }
  int rest = 3, cnt1 = 0, cnt2 = n - 2;
  for (int i = 0; i < n - 1; i++) {
    int u = edges[i].first, v = edges[i].second;
    if ((u == p || v == p) && rest) {
      ans[i] = cnt1++;
      rest--;
    } else
      ans[i] = cnt2--;
  }
  for (int i = 0; i < n - 1; i++) cout << ans[i] << '\n';
  return 0;
}