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;
vector<long long> gr[100005];
map<pair<long long, long long>, long long> mp;
long long visited[100005];
long long value = 0;
long long n, num = 1;
void dfs(long long curr) {
  visited[curr] = 1;
  for (auto it : gr[curr]) {
    if (visited[it] == 0) {
      if (gr[it].size() == 1) {
        mp[{curr, it}] = value;
        mp[{it, curr}] = value;
        value++;
      }
      dfs(it);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long x, y;
  cin >> n;
  long long root = -1;
  vector<pair<long long, long long>> vec;
  memset(visited, 0, sizeof(visited));
  for (long long i = 0; i < n - 1; i++) {
    cin >> x >> y;
    if (root == -1) root = x;
    gr[x].push_back(y);
    gr[y].push_back(x);
    vec.push_back({x, y});
  }
  dfs(root);
  for (auto it : vec) {
    if (mp.find({it.first, it.second}) != mp.end()) {
      cout << mp[{it.first, it.second}] << "\n";
    } else {
      cout << value << "\n";
      value++;
    }
  }
}