A triangulation of a polygon is a set of triangles with vertices at the vertices of a polygon. These triangles must not overlap and must cover the whole polygon.

We define a polygon cut as a straight line separating the polygon into two pieces. Given a triangulated convex polygon, where each triangle has some color, find the maximal number of cuts one can do so that no two points of the same color end up in two different pieces.

입력

• The first line contains the number of vertices, n. Vertices are numbered with unique integers between 1 and n.
• Each of the next n - 2 lines contains four integer numbers a, b, c and d (1 ≤ a,b,c,d ≤ n), meaning that the triangle which has its vertices in a, b and c has the color d. a, b and c are three different vertices.

출력

입출력 예

입력

5
1 2 3 2
4 5 1 1
3 1 4 2

출력

1

입력

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

출력

0

Constraints

출처: boi 2009