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
from collections import deque
input = stdin.buffer.readline

n = int(input())
d = [0] * (n+1)
g = [[] for _ in range(n+1)]
l = []
for _ in range(1, n):
	u, v = map(int, input().split())
	l.append((u, v))
	g[u].append(v)
	g[v].append(u)
	d[u] += 1
	d[v] += 1
q = deque()
for i in range(1, n+1):
	if d[i] == 1:
		q.append(i)
a = dict()
color = 0
while q:
	u = q.popleft()
	d[u] -= 1
	for v in g[u]:
		if (u, v) not in a:
			a[(u, v)] = a[(v, u)] = color
			color += 1
		d[v] -= 1
		if d[v] == 1:
			q.append(v)
print("\n".join(str(a[_]) for _ in l))