{"problem":{"name":"Convex Quadrilateral","description":{"content":"Consider a two-dimensional coordinate plane, where the $x$\\-axis is oriented to the right, and the $y$\\-axis is oriented upward. In this plane, there is a quadrilateral without self-intersection.   Th","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc266_c"},"statements":[{"statement_type":"Markdown","content":"Consider a two-dimensional coordinate plane, where the $x$\\-axis is oriented to the right, and the $y$\\-axis is oriented upward.\nIn this plane, there is a quadrilateral without self-intersection.  \nThe coordinates of the four vertices are $(A_x,A_y)$, $(B_x,B_y)$, $(C_x,C_y)$, and $(D_x,D_y)$, in counter-clockwise order.\nDetermine whether this quadrilateral is convex.\nHere, a quadrilateral is convex if and only if all four interior angles are less than $180$ degrees.\n\n## Constraints\n\n*   $-100 \\leq A_x,A_y,B_x,B_y,C_x,C_y,D_x,D_y \\leq 100$\n*   All values in input are integers.\n*   The given four points are the four vertices of a quadrilateral in counter-clockwise order.\n*   The quadrilateral formed by the given four points has no self-intersection and is non-degenerate. That is,\n    *   no two vertices are at the same coordinates;\n    *   no three vertices are colinear; and\n    *   no two edges that are not adjacent have a common point.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$A_x$ $A_y$\n$B_x$ $B_y$\n$C_x$ $C_y$\n$D_x$ $D_y$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc266_c","tags":[],"sample_group":[["0 0\n1 0\n1 1\n0 1","Yes\n\nThe given quadrilateral is a square, whose four interior angles are all $90$ degrees. Thus, this quadrilateral is convex.\n![image](https://img.atcoder.jp/abc266/cda66d9b9f4291781d1ce47f59f29ab0.png)"],["0 0\n1 1\n-1 0\n1 -1","No\n\nThe angle $A$ is $270$ degrees. Thus, this quadrilateral is not convex.\n![image](https://img.atcoder.jp/abc266/2927f9f67e2cb7c35aeab05269b6fcc2.png)"]],"created_at":"2026-03-03 11:01:14"}}