Zublicanes and Mumocrates

题意翻译

一棵树上有n<=5000个节点，把每个节点染成黑色或白色，要求叶子节点一半是黑色，一半是白色，求在满足要求的情况下，最小的两端颜色不同的边数

题目描述

It's election time in Berland. The favorites are of course parties of zublicanes and mumocrates. The election campaigns of both parties include numerous demonstrations on $ n $ main squares of the capital of Berland. Each of the $ n $ squares certainly can have demonstrations of only one party, otherwise it could lead to riots. On the other hand, both parties have applied to host a huge number of demonstrations, so that on all squares demonstrations must be held. Now the capital management will distribute the area between the two parties. Some pairs of squares are connected by $ (n-1) $ bidirectional roads such that between any pair of squares there is a unique way to get from one square to another. Some squares are on the outskirts of the capital meaning that they are connected by a road with only one other square, such squares are called dead end squares. The mayor of the capital instructed to distribute all the squares between the parties so that the dead end squares had the same number of demonstrations of the first and the second party. It is guaranteed that the number of dead end squares of the city is even. To prevent possible conflicts between the zublicanes and the mumocrates it was decided to minimize the number of roads connecting the squares with the distinct parties. You, as a developer of the department of distributing squares, should determine this smallest number.

输入输出格式

输入格式

The first line of the input contains a single integer $ n $ ( $ 2<=n<=5000 $ ) — the number of squares in the capital of Berland. Next $ n-1 $ lines contain the pairs of integers $ x,y $ ( $ 1<=x,y<=n,x≠y $ ) — the numbers of the squares connected by the road. All squares are numbered with integers from $ 1 $ to $ n $ . It is guaranteed that the number of dead end squares of the city is even.

输出格式

Print a single number — the minimum number of roads connecting the squares with demonstrations of different parties.

输入输出样例

输入样例 #1

8
1 4
2 4
3 4
6 5
7 5
8 5
4 5

输出样例 #1

1

输入样例 #2

5
1 2
1 3
1 4
1 5

输出样例 #2

2