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 = 200005;
int n;
int a[N], b[N], c[N];
void gao() {
  int p = -1, l = 0, r = n - 2;
  for (int i = 1; i <= n; i++)
    if (c[i] >= 3) {
      p = i;
      break;
    }
  if (p == -1) {
    for (int i = 0; i < n - 1; i++) printf("%d\n", i);
    return;
  }
  for (int i = 0; i < n - 1; i++) {
    if (a[i] == p || b[i] == p)
      printf("%d\n", l++);
    else
      printf("%d\n", r--);
  }
}
int main() {
  while (~scanf("%d", &n)) {
    memset(c, 0, sizeof(c));
    for (int i = 0; i < n - 1; i++) {
      scanf("%d %d", &a[i], &b[i]);
      c[a[i]]++, c[b[i]]++;
    }
    gao();
  }
  return 0;
}