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 collections import Counter,OrderedDict
from sys import stdin
n = int(stdin.readline())
dct = Counter()
dct1 = OrderedDict()
for _ in range(n-1):
    x = tuple(map(int,stdin.readline().split()))
    dct1[x] = -1
    dct[x[0]]+=1
    dct[x[1]]+=1
co = 0
for r in dct:
    if dct[r] >= 3:
        for x in dct1:
            if x[0] == r or x[1] == r:
                dct1[x] = co
                co += 1
        break
for r in dct1.keys():
    if dct1[r] == -1:
        dct1[r] = co
        co += 1
for k in dct1.values():
    print(k)