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;
map<pair<long long, long long>, long long> mp;
long long n;
long long dfs(long long root, long long par, vector<vector<long long> > &g) {
  long long children = 1;
  for (int i = 0; i < g[root].size(); i++) {
    if (g[root][i] == par) continue;
    long long temp = dfs(g[root][i], root, g);
    children += temp;
    mp[make_pair(root, g[root][i])] = temp * (n - temp);
  }
  return children;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n;
  vector<vector<long long> > g(n + 1);
  long long a, b;
  vector<pair<long long, long long> > ans;
  for (int i = 0; i < n - 1; i++) {
    cin >> a >> b;
    g[a].push_back(b);
    g[b].push_back(a);
    ans.push_back(make_pair(a, b));
  }
  dfs(1, 0, g);
  vector<pair<long long, pair<long long, long long> > > vec;
  for (auto it : mp) {
    pair<long long, long long> p = it.first;
    long long val = it.second;
    vec.push_back(make_pair(val, p));
  }
  sort(vec.begin(), vec.end());
  map<pair<long long, long long>, long long> mapp;
  long long x = 0;
  for (auto i : vec) {
    mapp[i.second] = x++;
  }
  for (auto i : ans) {
    if (mapp.find(i) != mapp.end())
      cout << mapp[i] << endl;
    else if (mapp.find(make_pair(i.second, i.first)) != mapp.end())
      cout << mapp[make_pair(i.second, i.first)] << endl;
  }
}