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 + 15;
int n;
vector<pair<int, int>> adj[MAXN];
int par[MAXN];
int ver;
int ans[MAXN];
bool mark[MAXN];
void dfs(int v = 1, int p = -1);
int32_t main() {
  memset(ans, -1, sizeof(ans));
  cin >> n;
  for (int i = 0, u, v; i + 1 < n; i++) {
    cin >> u >> v;
    adj[u].push_back({v, i});
    adj[v].push_back({u, i});
  }
  if (n < 4) {
    if (n == 2) return cout << "0\n", false;
    return cout << "0 1\n", false;
  }
  for (int i = 0; i < n; i++)
    if (adj[i].size() > 2) ver = i;
  if (!ver) {
    for (int i = 0; i < n - 1; i++) {
      if (!i)
        cout << i << ' ';
      else if (i > 1)
        cout << i << ' ';
    }
    return cout << "1\n", false;
  }
  int id = 0;
  for (auto u : adj[ver]) ans[u.second] = id++;
  for (int i = 0; i + 1 < n; i++)
    if (ans[i] == -1) ans[i] = id++;
  for (int i = 0; i < n - 1; i++) cout << ans[i] << ' ';
  return cout << '\n', false;
}