Description

Consider a tree with N vertices, numbered from 1 to N. Add, if it is possible, a minimum number of edges thus every vertex belongs to exactly one cycle.

Input

The input has the following structure:

N x(1) y(1) x(2) y(2) ... x(N-1) y(n-1) N (3 <= N <=100) is the number of vertices. x(i) and y(i) (x(i), y(i) are integers, 1 <= x(i), y(i) <= N) represent the two vertices connected by the i-th edge.

Output

The output will contain the value -1 if the problem doesn't have a solution, otherwise an integer, representing the number of added edges.

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

2

Source

Romania OI 2002