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 PYTHON3):

Solution:
from sys import stdin
import sys

tt = 1

for loop in range(tt):

    n = int(stdin.readline())

    lis = [ [] for i in range(n)]
    for i in range(n-1):
        u,v = map(int,stdin.readline().split())
        u -= 1
        v -= 1

        lis[u].append((v,i))
        lis[v].append((u,i))

    one = []
    for i in range(n):
        if len(lis[i]) == 1:
            one.append(i)

    ans = [None] * (n-1)
    cnt = 0
    for i in one:
        for v,ind in lis[i]:
            if ans[ind] == None:
                ans[ind] = cnt
                cnt += 1

    for i in range(n-1):
        if ans[i] == None:
            ans[i] = cnt
            cnt += 1

    print ("\n".join(map(str,ans)))