Clear the bay! Reloading...
The project to deliver carrot juice while bypassing Krylandia is ongoing. However, the pine-flavored carrot juice, essential for the Krylandians, is still transported by sea using specially equipped carrot juice barges.
During the unloading of one of these barges, an unusual incident occurred once again. For reasons still unclear, most of the delivered juice spilled into the open sea during the transfer from the barge to the shore. This poses two main issues: firstly, the decomposition of the juice into its components and settling on the seabed could lead to an ecological disaster. Secondly, payment is still required for the lost juice, as the cargo had already reached the port and unloading had begun.
Fortunately, there is some good news, though there is also a piece of not-so-good news. Let's start with the good news. Firstly, the leakage was quickly detected and contained, with the area of the spilled juice enclosed by a special net shaped like a convex polygon. Secondly, due to its physicochemical properties, the spilled juice is a homogeneous liquid with excellent fluidity and is less dense than seawater. It currently forms a uniform layer on the water's surface.
The not-so-good news is that the Krylandians lack the technical means to collect the entire mass of carrot juice before its components begin to settle on the seabed, potentially causing another ecological disaster. However, Krylandian engineers have calculated that if the spill is divided into two equal masses, they can connect two suction pump hoses to the center of mass of each resulting section. Thanks to the juice's excellent fluidity, this would allow them to collect all the spilled liquid before it settles. However, the Krylandians' current technical capabilities only allow for operations where the line dividing the spill into 2 parts is perpendicular to the OX axis (shore).
Your task is to determine the x-coordinate of the point to begin dividing the localized spill into two equal parts. Once this is done, the command "Clear the bay!" will be given, and the process of saving the Krylandians from an ecological disaster will be successfully completed.
Input
The first line specifies the number of vertices of the enclosing net n (3 ≤ n ≤ 250). The next n lines provide the vertices of the polygon x_i and y_i (|x_i|, |y_i| ≤ 1000), listed in the order of traversal. The input data is guaranteed to be correct, ensuring the polygon is convex.
Output
Output the x-coordinate of the point on the shore to start dividing the spilled juice into two equal parts. The answer must be given with a precision of at least 6 decimal places.