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:

class Solution():
    def __init__(self):
        pass
    def s(self):
        n = int(input())
        c = {}
        edges = []
        f, l = 0, n-2
        for i in range(n-1):
            u, v = map(int, input().split())
            edges.append((u,v))
            c.setdefault(u, 0)
            c.setdefault(v, 0)
            c[u] += 1
            c[v] += 1
        for i in edges:
            if(c[i[0]]==1 or c[i[1]]==1):
                print(f)
                f += 1
            else:
                print(l)
                l -= 1

if __name__ == "__main__":
    c = Solution()
    c.s()