문제<\/h2>
There is no generally accepted standard of calculating the center point of some territory. This fact is widely used to promote different places. You can always find a meaning for the word "center", according to which your city would be the center of the country! Gloria decided to develop one universal standard and find the true center.<\/p>
Consider any point inside a convex polygon, and any direction. There is a unique segment that passes through the point, is parallel to the direction, and has both ends on the boundary of the polygon. The point divides the segment into two parts. The direction imbalance<\/em> is defined as the ratio of the length of the bigger part to the length of the smaller part. The imbalance<\/em> of the point is the maximum direction imbalance over all directions. <\/p>
Gloria finds this value interesting, and wants to define the Grand center<\/em> of a convex polygon as the point inside it which has the minimum possible imbalance. Help her to calculate the imbalance of the Grand center of a given polygon.<\/p>

입력<\/h2>
The first line contains a single integer $n<\/mi><\/mrow>n<\/math><\/span><\/span> n<\/span><\/span><\/span><\/span> --- the number of vertices of the given convex polygon (3<\/mn>\leq<\/mo>n<\/mi>\leq<\/mo>10<\/mn><\/mtext>000<\/mn><\/mrow>3 \le n \le 10\,000<\/math><\/span><\/span> 3<\/span> <\/span> \leq<\/span> <\/span><\/span> <\/span> n<\/span> <\/span> \leq<\/span> <\/span><\/span> <\/span> 10<\/span> <\/span> 000<\/span><\/span><\/span><\/span>).<\/p> The i<\/mi><\/mrow>i<\/math><\/span><\/span> i<\/span><\/span><\/span><\/span>-th of the following n<\/mi><\/mrow>n<\/math><\/span>$