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:
from collections import deque


def main():
    n = int(input())

    graph = []
    for i in range(n):
        graph.append(set())

    edges_list = []
    for i in range(n - 1):
        edges_list.append(tuple(map(lambda x: int(x) - 1, input().split())))
        graph[edges_list[-1][0]].add(edges_list[-1][1])
        graph[edges_list[-1][1]].add(edges_list[-1][0])

    queue_of_vertex = deque()
    for i in range(n):
        if len(graph[i]) == 1:
            queue_of_vertex.append(i)

    count = 0
    edges = {}
    while len(queue_of_vertex) > 0:
        vertex = queue_of_vertex.popleft()
        for to in graph[vertex]:
            graph[to].remove(vertex)

            edges[vertex, to] = count
            edges[to, vertex] = count
            count += 1

            if len(graph[to]) == 1:
                queue_of_vertex.append(to)

        graph[vertex].clear()

    for element in edges_list:
        print(edges[element])


if __name__ == '__main__':
    main()