Persimmon

As autumn deepens, the persimmon tree in our garden has borne fruit again this year. However, the weather was not good this year, so there were only three fruits. The sun shone from the top of the persimmon tree and created shadows on the ground, which were circular and overlapped or separated depending on the position of the sun.

Write a program which reads the information about the shadows of each of the three persimmon fruits and finds the area of the shadows. The shadows of the three persimmon fruits all have the same radius.

Input

The input is given in the following form

$r$
$x_1$ $y_1$
$x_2$ $y_2$
$x_3$ $y_3$

In the first line, the radius of the circle representing the shade of the three persimmon fruits $r$ ($1 \leq r \leq 500$) is given as an integer. In the next three lines, the coordinates $x_i,y_i$ ($0 \leq x_i,y_i \leq 500$) of the center of the $i$-th circle are given as integers. The coordinates of the centers of all the circles are different (if $i \ne j$, then $x_i \ne x_j$ or $y_i \ne y_j$).

Output

Output the shaded area of the persimmon fruit as a real number in a line. The error must not exceed plus or minus 0.00001.

Sample Input and Output

Sample Input 1

2
0 0
2 0
1 5

Sample Output 1

32.7856330486

Sample Input 2

3
3 2
5 2
4 5

Sample Output 2

55.2157319565

 

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