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
def input():
	return sys.stdin.readline()[:-1]

n = int(input())
adj = [[] for _ in range(n)]
for i in range(n-1):
	u, v = map(int, input().split())
	adj[u-1].append((v-1, i))
	adj[v-1].append((u-1, i))

if max([len(x) for x in adj]) <= 2:
	print(*list(range(n-1)), sep="\n")
else:
	ans = [-1 for _ in range(n-1)]
	for i in range(n):
		if len(adj[i]) > 2:
			ans[adj[i][0][1]] = 0
			ans[adj[i][1][1]] = 1
			ans[adj[i][2][1]] = 2
			break
	tmp = 3
	for i in range(n-1):
		if ans[i] < 0:
			ans[i] = tmp
			tmp += 1
	print(*ans, sep="\n")