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:
import sys

def func(n,graph,kaunsa,d):
    cnt = 0
    ans = []
    for i in range(1, n+1):
        if len(graph[i])==1:
            cnt+= 1
    if cnt<3:
        for i in range(n-1):
            ans.append(i)
    else:
        for i in range(1, n+1):
            if len(graph[i])==1:
                not_found = str(i) + ' ' + str(graph[i][0])
                q = str(graph[i][0]) + ' ' + str(i)
                # q = q[-1::-1]
                # q = str(q[0])+' '+str(q[1])
                if not_found in d:
                    d[not_found] = 10**10
                else:
                    d[q] = 10**10
        here = cnt
        come = 0
        for i in kaunsa:
            if d[i] != 10**10:
                ans.append(here)
                here += 1
            else:
                ans.append(come)
                come += 1
    for i in ans:
        sys.stdout.write(str(i)+'\n')

n = int(sys.stdin.readline().rstrip().lstrip())
graph = [[] for i in range(n+1)]
kaunsa = []
d = {}
for i in range(n-1):
    u,v = list(map(int,sys.stdin.readline().rstrip().lstrip().split()))
    graph[u].append(v)
    graph[v].append(u)
    d[str(u)+' '+str(v)] = 1
    kaunsa.append(str(u)+' '+str(v))
ans = func(n,graph,kaunsa,d)