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
input = sys.stdin.readline

N = int(input())
graph = [[] for _ in range(N)]
Edges = {}
for i in range(N-1):
    a, b = map(int, input().split())
    a -= 1; b -= 1
    graph[a].append(b)
    graph[b].append(a)
    Edges[str(a) + "," + str(b)] = i
    Edges[str(b) + "," + str(a)] = i

ans = [-1]*(N-1)
ind = 0
for n in range(N):
    if len(graph[n]) >= 3:
        for np in graph[n]:
            e = Edges[str(n) + "," + str(np)]
            ans[e] = ind
            ind += 1
            if ind >= 3:
                break
        break

for n in range(N-1):
    if ans[n] == -1:
        ans[n] = ind
        ind += 1

print(*ans, sep="\n")