you give n point plane the polygon form n point strictly convex polygon convex collinear point ie lie straight line the point number 1 n clockwise orderWe define distance point p_1 x_1 y_1 p_2 x_2 y_2 Manhattan distance dp_1 p_2 x_1 x_2 y_1 y_2Furthermore define perimeter polygon sum Manhattan distance adjacent pair point point polygon order p_1 p_2 ldot p_k k geq 3 perimeter polygon dp_1 p_2 dp_2 p_3 ldot dp_k p_1For parameter k let consider polygon form give set point have k vertex polygon selfintersecte for polygon let consider perimeter over perimeter define fk maximal perimeterplease note check polygon selfintersecte edge polygon draw straight line for instance follow picture in middle polygon order point p_1 p_3 p_2 p_4 valid selfintersecting polygon the right polygon edge resemble Manhattan distance order selfintersecte consider edge straight line the correct way draw polygon p_1 p_2 p_3 p_4 leave polygonYour task compute f3 f4 ldot fn in word find maximum possible perimeter possible number point ie 3 n