Intersection

Write a program that computes the area of intersection of the circle and a square with sides parallel to the axes.

Input

The first line contains three numbers, separated by space - the coordinates of the center of the circleX_0 and Y_0) and radius of the circle R. The second row contains three numbers, separated by space - the coordinates of the lower left corner (X and Y) and the size of the square S. All numbers are in the range of 1 to 20.

Output

Display single number - the area of intersection of the circle and square with two decimal signs.

Examples