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 atexit
import io
import sys
 
_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER
 
 
@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())

data = input().rstrip().split()
n = int(data[0])

edges = []

g = {i+1: [] for i in range(n)}

leafes = set()

for _ in range(n-1):
    data = input().rstrip().split()
    a, b = int(data[0]), int(data[1])
    a, b = sorted([a, b])
    edges.append((a, b))
    g[a].append(b)
    g[b].append(a)

for k, v in g.items():
    if len(leafes) == 3:
        break

    if len(v) == 1:
        e = sorted([k, v[0]])
        leafes.add(tuple(e))

counter = len(leafes)
l_counter = 0
to_print = []

for edge in edges:
    a, b = edge

    if edge in leafes:
        to_print.append(l_counter)
        l_counter += 1

    else:
        to_print.append(counter)
        counter += 1

for p in to_print:
    print(p)