Cannon

Petya, a scout, has uncovered crucial information about the location of an enemy's strategic target. To strike this target, a cannon situated on enemy territory can be utilized. However, Petya has only managed to breach the first level of the combat system's security, allowing him to control the timing of the cannon's shot. Unfortunately, he does not know the cannon's aim direction or elevation. From indirect sources, it is understood that the cannon can aim in any direction with equal probability, and the probability of hitting a point at a distance (x) from the cannon follows an exponential distribution (exp(-x)). Since Petya needs to neutralize the strategic target as quickly as possible, he has asked you to estimate the probability of the cannon hitting the target. If the probability is low, a more reliable method can be employed without risking exposure.

Input

The first line contains the number (n) ((3 $\le$ n $\le$ 300)) — the number of nodal points of the enemy target, which forms a non-degenerate convex polygon. The data includes noise, and some points are unnecessary for defining the object's shape, but each vertex of the polygon has at least one nodal point. Following this, each line contains two integers (x_i), (y_i) ((-500 $\le$ x_i, y_i $\le$ 500)) — the coordinates of the nodal points.

Output

Output a single number with at least (6) decimal places — the probability of the cannon hitting the enemy target.

Examples