Fisherman's net#4795
Seva sometimes engages in industrial fishing to supplement his family income. Modern fishermen, especially those at sea, are quite different from those at the end of the last century. Now, they have access to powerful computer fish finders that can detect fish underwater and display their coordinates.
Having located a school of fish on the fish finder's screen, Seva is now trying to determine the minimum length of net required to catch the entire school. Assume that the fish are stationary (they have just eaten). Seva can use nets of any size, but all nets are only available in lengths that are multiples of meters, as that is the only type sold at the underground Kryland market. The nets are made with advanced technology, allowing them to bend at any angle without losing their strength.
Help Seva quickly calculate the minimum length of net he must deploy before the fish wake up and swim away.
The first line contains the number of fish detected by the fish finder, (1 \leq N \leq 20000). Each of the next lines contains two integers, the coordinates of each fish: x_i and y_i. The absolute values of the coordinates do not exceed .
Output a single number: the minimum length of the net Seva needs to cast to catch the school.
Example 1