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

_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__


def go():
    n = int(input())
    # n, h, l, r = map(int, input().split())
    # a = list(map(int, input().split()))

    ranks = [0]*n
    e = [0]*n
    for i in range(n-1):
        x,y = map(int, input().split())
        x,y = x-1,y-1
        e[x]=i
        e[y]=i
        ranks[x]+=1
        ranks[y]+=1
    leafs= [i for i in range(n) if ranks[i]==1]
    if len(leafs)==2:
        return '\n'.join(map(str,range(n-1)))
    else:
        vals = [-1]*(n-1)
        for ind,i in enumerate(leafs[:3]):
            j = e[i]
            vals[j]=ind
        ind=3
        for i in range(n-1):
            if vals[i]<0:
                vals[i]=ind
                ind+=1
        return '\n'.join(map(str, vals))

# t = int(input())
# ans=[]
for _ in range(1):
    print(go())
# print('\n'.join(ans))