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():
    n = int(input())
    turns = []
    dct = dict()
    to_spec = n
    for i in range(n - 1):
        a, b = map(int, input().split())
        turns.append((a, b))
        if a in dct:
            if dct[a] == 1:
                dct[a] += 1
                to_spec -= 1
        else:
            dct[a] = 1
        if b in dct:
            if dct[b] == 1:
                dct[b] += 1
                to_spec -= 1
        else:
            dct[b] = 1

    to_add1 = 0
    line = ""
    for i in turns:
        if dct[i[0]] == 1 or dct[i[1]] == 1:
            line += str(to_add1) + "\n"
            to_add1 += 1
        else:
            line += str(to_spec) + "\n"
            to_spec += 1
    print(line)


if __name__ == "__main__":
    t = 1
    for i in range(t):
        main()