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())
    input_edges = dict()
    edges = dict()
    for i in range(n-1):
        a, b = list(map(int, input().split()))
        input_edges[(a, b)] = i
        input_edges[(b, a)] = i
        if a in edges:
            edges[a].append(b)
        else:
            edges[a] = [b]
        if b in edges:
            edges[b].append(a)
        else:
            edges[b] = [a]
        
    degrees = dict()
    for i in range(1, n+1):
        l = len(edges[i])
        if l in degrees:
            degrees[l].append(i)
        else:
            degrees[l] = [i]
    
    values_degrees = [-1] * (len(input_edges)//2)
    
    start_degree = 0
    if 1 in degrees:
        for i in degrees[1]:
            node1 = i
            node2 = edges[i][0]
            j = input_edges[(node1, node2)]
            if values_degrees[j] == -1:
                values_degrees[j] = start_degree
                start_degree += 1

    for i in range(len(values_degrees)):
        if values_degrees[i] == -1:
            values_degrees[i] = start_degree
            start_degree += 1
        print(values_degrees[i])

    


if __name__ == "__main__":
    run()