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 functools

mod = 998244353
def ncr(n,r):
    r=min(r,n-r)
    a=functools.reduce(lambda x,y: (x*y), range(n,n-r,-1),1)
    b=functools.reduce(lambda x,y: (x*y), range(1,r+1),1)
    return a//b

"""
def func(arr, l, r, x):
    while(l<r):
        mid = (l+r)//2
        if arr[mid]+x > 0:
            r = mid
        else:
            l = mid+1
    return l

d = {}
i = 0
n = int(stdin.readline())
for _ in range(n-1):
    #x = int(stdin.readline())
    u, v = map(int, stdin.readline().split())
    #arr = list(map(int,stdin.readline().split())
    if u in d:
        d[u][0] += 1
        d[u][1].append(i)
    else:
        d[u] = [1, [i]]
        
    if v in d:
        d[v][0] += 1
        d[v][1].append(i)
    else:
        d[v] = [1, [i]]
    
    i += 1
ans = [-1]*(n-1)
val = 0
for ele in d:
    if d[ele][0]>=3:
        for item in d[ele][1]:
            if ans[item] == -1:
                ans[item] = val
                val += 1

for i in range(n-1):
    if ans[i] == -1:
        print(val)
        val += 1
    else:
        print(ans[i])