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 MOD = 1e9 + 7;
const int N = 1e6 + 10;
vector<int> adj[N];
vector<pair<int, int> > edges;
map<pair<int, int>, int> mm;
int degree[N];
vector<int> dtoe[N];
bool cmp(vector<int> a, vector<int> b) { return a.size() <= b.size(); }
int main() {
  int n, x, y;
  cin >> n;
  memset(degree, 0, sizeof degree);
  for (int i = 0; i < n - 1; i++) {
    cin >> x >> y;
    pair<int, int> xx = make_pair(min(x, y), max(x, y));
    edges.push_back(xx);
    adj[x].push_back(y);
    adj[y].push_back(x);
    degree[x]++;
    degree[y]++;
  }
  for (int i = 1; i <= n; i++) {
    dtoe[degree[i]].push_back(i);
  }
  int curw = 0;
  for (int i = 1; i <= n; i++) {
    for (auto x : dtoe[i]) {
      for (auto ed : adj[x]) {
        pair<int, int> xx = make_pair(min(x, ed), max(x, ed));
        if (mm.find(xx) == mm.end()) {
          mm[xx] = curw;
          curw++;
        }
      }
    }
  }
  for (auto xx : edges) {
    cout << mm[xx] << "\n";
  }
}