{"code":"icpc21roundedconvex","name":"Rounded Convex Hull","description":"On a 2D plane, there are $N$ circles and $M$ polygons. Find the perimeter of the convex hull of all these figures.\r\n\r\n

Input

\r\n\r\n- The first line of input contains 2 integers $N$ and $M (0 \\le N, M \\le 10^5\r\n, 1 \\le N + M)$, the number of circles and\r\npolygons.\r\n\r\n- The next $N$ lines, each has 3 numbers $x_i\r\n, y_i$ and $r_i$ which is the center of the circle and its radius $(|x_i|, |y_i| \\le 5 × 10^4, 0 \\le r_i \\le 5 × 10^4)$.\r\n\r\n- The next $M$ lines, each line start with an integer $p_i (p_i ≥ 1)$, the number of vertices in the polygon followed by $p_i$\r\npair of numbers $(x_i,1, y_i,1), ..., (x_i,p_i, y_i,p_i) (|x_{i,j}|, |y_{i,j}| \\le 5 × 10^4)$. \r\nTotal number of vertices on all polygons will\r\nnot exceeed $10^5$.\r\n\r\n

Output

\r\n\r\n- Output the perimeter of the convex hull. The answer is considered correct if precision error is less than $10^{−5}$\r\n.\r\n\r\n

Example

\r\n\r\n!!! question \"Test 1\"\r\n\r\n ???+ \"Input\"\r\n ```sample\r\n 3 2\r\n -14.123000 -1.456000 5.789000\r\n 0.123000 14.456000 4.789000\r\n -6.868686 20.456780 3.789285\r\n 1 5.123000 5.456000\r\n 2 6.879000 6.123000 7.456000 7.789000\r\n ```\r\n \r\n ???+ success \"Output\"\r\n ```sample\r\n 88.888888\r\n ```","points":400.0,"partial":false,"time_limit":1.0,"memory_limit":262144,"short_circuit":false,"allowed_languages":[3,4,34,36,37,5,6,11,12,14,28,2,38,39,9,18,17,29,23,27,35,25,26,10,7,19,32,1,8,15,16,24,20,33,13,41,21,40],"is_public":true,"is_manually_managed":false,"permissions":{"can_edit":false}}