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 br[maxn];
int ind[maxn];
bool vaz[maxn];
vector<int> kraj;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  int a, b;
  for (int i = 0; i < n - 1; i++) {
    cin >> a >> b;
    a--;
    b--;
    br[a]++;
    br[b]++;
    ind[a] = i;
    ind[b] = i;
  }
  for (int i = 0; i < n; i++) {
    if (br[i] == 1) {
      kraj.push_back(i);
    }
  }
  if (kraj.size() == 2) {
    for (int i = 0; i < n - 1; i++) {
      cout << i << '\n';
    }
  } else {
    vaz[ind[kraj[0]]] = 1;
    vaz[ind[kraj[1]]] = 1;
    vaz[ind[kraj[2]]] = 1;
    int x = 0;
    int x1 = 3;
    for (int i = 0; i < n - 1; i++) {
      if (vaz[i]) {
        cout << x << '\n';
        x++;
      } else {
        cout << x1 << '\n';
        x1++;
      }
    }
  }
  return 0;
}