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 N = 2e5 + 100;
const int SQRTN = 320;
const int LOGN = 20;
const double PI = acos(-1);
const double TAU = 2 * PI;
int n;
vector<vector<int> > g;
vector<pair<int, int> > e;
map<pair<int, int>, int> idx;
int ans[N];
inline void solve() {
  cin >> n;
  g.resize(n + 1);
  memset(ans, -1, sizeof ans);
  for (int i = 1, a, b; i < n; i++) {
    scanf("%d%d", &a, &b);
    g[a].push_back(b);
    g[b].push_back(a);
    idx[make_pair(min(a, b), max(a, b))] = i;
  }
  int x = 0;
  for (int i = 1; i <= n; i++) {
    if (g[i].size() > 2) {
      ans[idx[make_pair(min(g[i][0], i), max(g[i][0], i))]] = 0;
      ans[idx[make_pair(min(g[i][1], i), max(g[i][1], i))]] = 1;
      ans[idx[make_pair(min(g[i][2], i), max(g[i][2], i))]] = 2;
      x = 3;
      break;
    }
  }
  for (int i = 1; i < n; i++) {
    if (ans[i] == -1)
      printf("%d\n", x++);
    else
      printf("%d\n", ans[i]);
  }
}
signed main() {
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}