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 main():
    data = input().rstrip().split()
    n = int(data[0])
    
    edges = []
    
    g = list([] for _ in range(n))
    
    leafes = list(False for _ in range(n))
    counter = 0
    
    for _ in range(n-1):
        a, b = sorted(map(int, input().split()))
        a, b = a-1, b-1
        edges.append((a, b))
        g[a].append(b)
        g[b].append(a)
    
    for k, v in enumerate(g):
        if counter == 3:
            break
    
        if len(v) == 1:
            leafes[k] = True
            counter += 1
    
    l_counter = 0
    to_print = []
    
    for edge in edges:
        a, b = edge
    
        if leafes[a] or leafes[b]:
            to_print.append(l_counter)
            l_counter += 1
    
        else:
            to_print.append(counter)
            counter += 1
    
    print('\n'.join(str(foo) for foo in to_print))
    
main()