{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003ci\u003eA convex polygon is a simple polygon whose interior is a convex set.[1] The following properties of a simple polygon are all equivalent to convexity:\u003cbr\u003e\u003cbr\u003e\n Every internal angle is less than 180 degrees. \u003cbr\u003e\n Every line segment between two vertices remains inside or on the boundary of the polygon. \u003cbr\u003e\n A simple polygon is strictly convex if every internal angle is strictly less than 180 degrees. Equivalently, a polygon is strictly convex if every line segment between two nonadjacent vertices of the polygon is strictly interior to the polygon except at its endpoints.\u003cbr\u003e\n \u003cpre\u003e —from Wikipedia\u003c/pre\u003e\u003c/i\u003e\n\u003cbr\u003e\n There are two convex polygons, A and B, on the plane. We want to know whether these two polygons intersection or overlap after every time we moving them.\n\u003cbr\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The input contains multiple test cases, for each test case, the first line is two integers, N(N ≦ 50000), M (M ≦ 50000)and K(K ≦ 10000), N is the number of points of convex A, M is the number of points of convex B, K is the number of move operation. N + M + K lines follow, the first N lines describes the coordinates of convex A in anti-clock wise, then the next M lines describes the coordinates of convex B in anti-clock wise, the last K lines is the move operations. “A x y” means move A with (x, y). “B x y” means move B with (x, y)."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, the output should contain K+1 lines, the first line is whether A and B intersect or overlap in the beginning, then K lines follow. Output Yes or No to figure out whether A and B intersect or overlap or not after each operation."}},{"title":"Sample Input","value":{"format":"HTML","content":"\u003cpre\u003e3 3 3\r\n0.0 0.0\r\n2.0 0.0\r\n1.0 1.0\r\n2.0 0.0\r\n4.0 0.0\r\n3.0 1.0\r\nB -1.0 0.0\r\nB 0.5 0.5\r\nA -1.0 0.5\r\n\u003c/pre\u003e"}},{"title":"Sample Output","value":{"format":"HTML","content":"\u003cpre\u003eYes\r\nYes\r\nYes\r\nNo\r\n\u003c/pre\u003e"}}]}