Cautious judge#1050
Tomorrow, a football match will take place between two famous teams: Blue Stars and Red Eagles. The match will be held on a field with length and width . The referee will be a fourth-generation professional football referee, Benjamin.
Being a referee is a responsible and sometimes dangerous job. Therefore, Benjamin decided to work through some game scenarios that may occur during tomorrow's match.
Consider a situation where player makes a pass to player , that is, the ball is passed along the line segment joining the points where the players are located. On the one hand, the referee should have a good view of the events during the pass. On the other hand, according to safety requirements, the referee cannot be too close to the ball. Therefore, during the pass, the referee must be at a distance of at least and at most from any possible position of the ball. It is assumed that while the ball is moving, the referee stands in one place. Of course, the referee must always be within the field during the match.
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Because these conditions are quite complex, even an experienced referee sometimes finds it hard to determine where to stand at the moment of the pass. For this reason, before the match, Benjamin wants to practice determining the regions where he can stand for different initial conditions. To compare his solution with the correct one, he needs a program that, given the field dimensions, the coordinates of the players, and the numbers and , finds the area of regions where the referee can be. Help him!
The first line contains two positive integers and (1 \leq L, W \leq 100) — the length and width of the field.
The second line contains integers X_A, Y_A, X_B, Y_B — the coordinates of players and , respectively. Since the players are on the field, 0 \leq X_A, X_B \leq L, 0 \leq Y_A, Y_B \leq W.
The third line contains numbers and (0 < r < R < 100). It is given that R \leq D, where is the distance between players and .
Output the answer to the problem with an accuracy of 10^{-6}.
Example 1