In the Clouds

In the "Surreal" game engine, clouds are generated as convex polyhedra with triangular faces. For example, an octohedron has 8 triangular faces:

Given the points that make up each face of a cloud, what is its volume?

Input

The first line consists of an integer ~N~ ~(1 \leq N \leq 10^5)~, the number of faces on the cloud.

The next ~N~ lines contain 3 points on the cloud, in the form ~X_1~ ~Y_1~ ~Z_1~, ~X_2~ ~Y_2~ ~Z_2~, ~X_3~ ~Y_3~ ~Z_3~, representing a face of the cloud. ~(0 \leq X, Y, Z \leq 10^8)~

Note: Each cloud is guaranteed to be a complete, convex 3D polygon made of triangular faces.

Output

Output the volume of the cloud, in units³, to 4 decimal places.

Example

Input

8
2 1 1 1 2 1 1 1 2
2 1 1 1 0 1 1 1 2
0 1 1 1 2 1 1 1 2
0 1 1 1 0 1 1 1 2
2 1 1 1 2 1 1 1 0
2 1 1 1 0 1 1 1 0
0 1 1 1 2 1 1 1 0
0 1 1 1 0 1 1 1 0

Output

1.3333

The octohedron shown above has an area of 1.3333 units³.