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 answer(nodeCount, nodeRelationship) :
    if len(nodeRelationship) <= 2 :
        return "\n".join([str(i) for i in range(len(nodeRelationship))])

    graph = [0 for i in range(nodeCount)]
    labelStickers = [i for i in range(len(nodeRelationship)-1, 2, -1)]
    smallLabelStickers = [0, 1, 2]
    labels = [-1 for i in range(len(nodeRelationship))]

    for i in range(len(nodeRelationship)) :
        graph[nodeRelationship[i][0]-1] += 1
        graph[nodeRelationship[i][1]-1] += 1

    for i in range(len(graph)) :
        if graph[i] >= 3 :
            nodeIndex = i+1
            for j in range(len(nodeRelationship)) :
                nr = nodeRelationship[j]
                if (nr[0] == nodeIndex or nr[1] == nodeIndex) and len(smallLabelStickers) > 0 :
                    labels[j] = smallLabelStickers.pop()
                else :
                    labels[j] = labelStickers.pop()
            break
    else :
        labels = labelStickers + smallLabelStickers
    
    return "\n".join([str(i) for i in labels])

nodeCount = int(input())
nodeRelationship = [0 for i in range(nodeCount-1)]
for i in range(nodeCount-1) :
    nodeRelationship[i] = list(map(int, input().split()))

print(answer(nodeCount, nodeRelationship))