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;
int n;
vector<int> q[100005];
int f, t;
int p[100005];
bool r;
int main() {
  cin >> n;
  for (int i = 1; i < n; i++) {
    scanf("%d%d", &f, &t);
    q[f].push_back(i), q[t].push_back(i);
  }
  for (int i = 1; i <= n; i++) {
    if (q[i].size() >= 3) {
      r = 1;
      for (int j = 0; j <= 2; j++) {
        p[q[i][j]] = j + 1;
      }
      break;
    }
  }
  if (r == 0) {
    for (int i = 0; i < n - 1; i++) {
      cout << i << endl;
    }
    return 0;
  }
  int cnt = 2;
  for (int i = 1; i <= n - 1; i++) {
    if (p[i] == 3) cout << 0 << endl;
    if (p[i] == 1) cout << 1 << endl;
    if (p[i] == 2) cout << 2 << endl;
    if (p[i] == 0) cout << ++cnt << endl;
  }
}