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
import heapq

n = int(input())

edges = {} # n -> [u, v]
nodes = {} # n -> # edges
label = {} # (u, v) -> label
heap = [] # (#edges, n)

orig = []

for line in sys.stdin.readlines():
	u, v = list(map(int, line.split()))
	orig.append((u, v))
	if u in edges:
		edges[u].append(v)
	else:
		edges[u] = [v]
		nodes[u] = 1
	if v in edges:
		edges[v].append(u)
	else:
		edges[v] = [u]
		nodes[v] = 1

for n in nodes:
	heap.append((len(edges[n]), n))
heapq.heapify(heap)

counter = 0
while len(heap) > 0:
	vals = heapq.heappop(heap)
	for e in edges[vals[1]]:
		if (vals[1], e) in label or (e, vals[1]) in label:
			continue
		label[(vals[1], e)] = counter
		label[(e, vals[1])] = counter
		counter += 1
for v in orig:
	print(label[v])