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 = 101010;
int deg[MAXN], n, e[MAXN];
vector<pair<int, int> > G[MAXN];
int main() {
  memset(e, -1, sizeof e);
  scanf("%d", &n);
  if (n == 2) {
    puts("0");
    return 0;
  }
  int z = 0;
  for (int i = 1; i < n; ++i) {
    static int u, v;
    scanf("%d%d", &u, &v);
    G[u].emplace_back(v, i - 1);
    G[v].emplace_back(u, i - 1);
    deg[u]++;
    deg[v]++;
  }
  queue<int> q;
  for (int i = 1; i <= n; ++i)
    if (deg[i] == 1) e[G[i][0].second] = z++;
  for (int i = 0; i < n - 1; ++i) {
    if (e[i] == -1) e[i] = z++;
    printf("%d\n", e[i]);
  }
  return 0;
}