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:
def run():
    n = int(input())
    edges = []
    graph = [0 for i in range(n)]
    for _ in range(n-1):
        u, v = map(int, input().split())
        edges.append([u-1, v-1])
        graph[u-1] += 1
        graph[v-1] += 1
    for k in range(n):
        if graph[k] >= 3:
            h = 0
            l = graph[k]
            for e in edges:
                if e[0] == k or e[1] == k:
                    print(h)
                    h += 1
                else:
                    print(l)
                    l += 1
            return 
        
    for i in range(n-1):
        print(i)

run()