Clear the bay! Reloading...#4797
The project to deliver carrot juice while bypassing Krylandia continues, but the pine-flavored carrot juice, vital for the Krylandians, is still supplied by sea in specially equipped carrot-juice barges.
During the unloading of one of the barges, an unusual incident occurred again: for unknown reasons, most of the delivered juice was spilled into the open sea during the transfer from the barge to the shore. Naturally, this presents several problems. Firstly, the decomposition of the juice and its settling on the seabed could result in an environmental disaster. Secondly, payment is still required for the lost juice because the cargo had already been delivered and unloading had started.
There is, however, both good and not-so-good news. The good news: the leak was promptly detected and contained; the affected area was enclosed by a special net in the form of a convex polygon. Moreover, due to its physicochemical properties, the spilled juice forms a homogeneous liquid with high fluidity and is less dense than seawater. As a result, it sits as a thin layer on the surface, uniformly within the net.
The not-so-good news is that the Krylandians lack the technical means to remove the entire mass before its components settle, risking another ecological problem. However, their engineers have determined that if the spot can be divided into two equal areas (by mass), it is possible to set up two pump hoses at the centers of mass of the respective halves and remove all the liquid before sedimentation begins, due to its excellent fluidity.
Currently, the Krylandians' technical means allow only such operations where the dividing line is perpendicular to the axis (the shore).
Your task is to find the -coordinate for the location along the shore to begin separating the localised spot into two equal parts. Of course, after this the command "Clear the bay!" will once again be heard, and the process of saving the Krylandians from an ecological disaster will once again be completed successfully.
The first line contains the number of vertices (3 \le n \le 250) of the convex polygon formed by the enclosing net. The next lines contain the coordinates x_i and y_i (|x_i|, |y_i| \le 1000) of the vertices of the polygon given in the order of traversal. It is guaranteed that the polygon is convex and the input is valid.
Output the -coordinate on the shore to begin dividing the spilled juice into two equal parts. The answer must be output with a precision of at least decimal places.
Example 1