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:
nodes = {}

if __name__ == '__main__':
    numNodes = int(input())
    nodes = {}
    mentioned = {}
    for i in range(1,numNodes+1):
        nodes[i] = set()
        mentioned[i] = []

    for _ in range(numNodes-1):
        edge = input().split(" ")
        mentioned[int(edge[0])].append(_)
        mentioned[int(edge[1])].append(_)
        nodes[int(edge[0])].add(int(edge[1]))
        nodes[int(edge[1])].add(int(edge[0]))
    
    triplet = -1
    for i in range(1,numNodes+1):
        if (len(mentioned[i]) >= 3):
            triplet = mentioned[i][:3]
    count = 3
    tripCount = 0
    if (triplet == -1):
        for i in range(numNodes-1):
            print(i)
    else:
        for i in range(numNodes-1):
            if i not in triplet:
                print(count)
                count += 1
            else:
                print(tripCount)
                tripCount += 1

"""6
1 2
1 3
2 4
2 5
5 6"""