{"problem":{"name":"One Fourth","description":{"content":"ABC 250 is a commemorable quarter milestone for Takahashi, who aims to hold ABC 1000, so he is going to celebrate this contest by eating as close to $1/4$ of a pizza he bought as possible. The pizza t","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc250_f"},"statements":[{"statement_type":"Markdown","content":"ABC 250 is a commemorable quarter milestone for Takahashi, who aims to hold ABC 1000, so he is going to celebrate this contest by eating as close to $1/4$ of a pizza he bought as possible.\nThe pizza that Takahashi bought has a planar shape of convex $N$\\-gon. When the pizza is placed on an $xy$\\-plane, the $i$\\-th vertex has coordinates $(X_i, Y_i)$.\nTakahashi has decided to cut and eat the pizza as follows.\n\n*   First, Takahashi chooses two non-adjacent vertices from the vertices of the pizza and makes a cut with a knife along the line passing through those two points, dividing the pizza into two pieces.\n*   Then, he chooses one of the pieces at his choice and eats it.\n\nLet $a$ be the quarter ($=1/4$) of the area of the pizza that Takahashi bought, and $b$ be the area of the piece of pizza that Takahashi eats. Find the minimum possible value of $8 \\times |a-b|$. We can prove that this value is always an integer.\n\n## Constraints\n\n*   All values in input are integers.\n*   $4 \\le N \\le 10^5$\n*   $|X_i|, |Y_i| \\le 4 \\times 10^8$\n*   The given points are the vertices of a convex $N$\\-gon in the counterclockwise order.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$X_1$ $Y_1$\n$X_2$ $Y_2$\n$\\dots$\n$X_N$ $Y_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc250_f","tags":[],"sample_group":[["5\n3 0\n2 3\n-1 3\n-3 1\n-1 -1","1\n\nSuppose that he makes a cut along the line passing through the $3$\\-rd and the $5$\\-th vertex and eats the piece containing the $4$\\-th vertex.  \nThen, $a=\\frac{33}{2} \\times \\frac{1}{4} = \\frac{33}{8}$, $b=4$, and $8 \\times |a-b|=1$, which is minimum possible."],["4\n400000000 400000000\n-400000000 400000000\n-400000000 -400000000\n400000000 -400000000","1280000000000000000"],["6\n-816 222\n-801 -757\n-165 -411\n733 131\n835 711\n-374 979","157889"]],"created_at":"2026-03-03 11:01:14"}}