Score : 1400 points
We will recursively define uninity of a tree, as follows: (Uni is a Japanese word for sea urchins.)
It can be shown that a tree of uninity k is also a tree of uninity k+1,k+2,..., and so forth.
You are given a tree consisting of N vertices. The vertices of the tree are numbered 1 through N, and the i-th of the N-1 edges connects vertices a_i and b_i.
Find the minimum k such that the given tree is a tree of uninity k.
The input is given from Standard Input in the following format:
N a_1 b_1 : a_{N-1} b_{N-1}
Print the minimum k such that the given tree is a tree of uninity k.
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A tree of uninity 1 consisting of vertices 1, 2, 3 and 4 can be constructed from the following: a tree of uninity 0 consisting of vertex 1, a tree of uninity 0 consisting of vertex 3, a tree of uninity 0 consisting of vertex 4, and vertex 2.
A tree of uninity 1 consisting of vertices 5 and 7 can be constructed from the following: a tree of uninity 1 consisting of vertex 5, and vertex 7.
A tree of uninity 2 consisting of vertices 1, 2, 3, 4, 5, 6 and 7 can be constructed from the following: a tree of uninity 1 consisting of vertex 1, 2, 3 and 4, a tree of uninity 1 consisting of vertex 5 and 7, and vertex 6.
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