Description

Calculate the length of the intersection of two circles in 3D space.

Input

There are no more than 10000 test cases. For each test case two lines of integer numbers are given, describing the two circles in 3D space respectively.

A circle in 3D space is described by 7 integer numbers – its radius r and two 3D coordinates. The first coordinate (x₁, y₁, z₁) is its center, while the second (x₂, y₂, z₂) represents the normal vector of the plane where the circle lies.

It is guaranteed that the two circles given are not parallel or coplanar.

1 ≤ r ≤ 10000, all the other input integers are in range [−10000,10000].

Output

Each case one line, the lengh of the intersection. The error between the result and the answer should not exceed 10⁻⁵.

Sample

1 0 0 0 0 0 1
1 1 1 0 1 1 0
1 0 0 0 0 0 1
2 1 0 0 1 1 1

0
1.414214

Hint