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

ans = [None] * (n - 1)
for u in range(n):
    if len(graph[u]) >= 3:
        v1 = graph[u][0]
        v2 = graph[u][1]
        v3 = graph[u][2]
        ans[d[(u, v1)]] = 0
        ans[d[(u, v2)]] = 1
        ans[d[(u, v3)]] = 2
        break

c = 3
for i in range(n - 1):
    if ans[i] is None:
        ans[i] = c % (n - 1)
        c += 1
print('\n'.join(map(str, ans)))