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 read_int():
    return int(input().strip())


def read_ints():
    return list(map(int, input().strip().split(' ')))


def solve():
    N = read_int()
    counts = [0]*N
    edges = []
    for _ in range(N-1):
        edge = read_ints()
        edge[0] -= 1
        edge[1] -= 1
        edges.append(edge)
        counts[edge[0]] += 1
        counts[edge[1]] += 1
    C = 0
    labels = [-1]*(N-1)
    for i, (u, v) in enumerate(edges):
        if counts[u] == 1 or counts[v] == 1:
            labels[i] = C
            C += 1
    for i in range(N-1):
        if labels[i] == -1:
            labels[i] = C
            C += 1
    for label in labels:
        print(label)


if __name__ == '__main__':
    solve()