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 long long INF = 1e9;
const long long MOD = 1e9 + 7;
const long long maxn = 1e5 + 7;
const long long maxm = 2e5 + 7;
struct Edge {
  int end, idx, label, vis;
};
vector<Edge> adj[maxn];
vector<int> deg[maxn];
int n, ans[maxn], vis[maxn];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  cin >> n;
  for (int i = 0; i <= n - 2; i++) {
    int u, v;
    cin >> u >> v;
    Edge e;
    e.idx = i;
    e.end = u;
    adj[v].push_back(e);
    e.end = v;
    adj[u].push_back(e);
  }
  for (int i = 1; i <= n; i++) {
    deg[adj[i].size()].push_back(i);
  }
  int maxUsed = 0;
  for (int d = 1; d <= n - 1; d++) {
    for (int u : deg[d]) {
      for (Edge e : adj[u]) {
        if (!vis[e.end]) {
          ans[e.idx] = maxUsed;
          maxUsed++;
        }
      }
      vis[u] = true;
    }
  }
  for (int i = 0; i <= n - 2; i++) {
    cout << ans[i] << endl;
  }
  return 0;
}