AT_ttpc2024_1_e ReTravel

On the $ xy $ -plane, there are $ N $ points labeled $ 1, 2, \dots, N $ . The coordinates of point $ i $ ( $ 1 \le i \le N $ ) are $ (X_i, Y_i) $ . There is a robot at the origin of this plane. Your task is to control the robot to visit all the points $ 1, 2, \dots, N $ **in this order**. The robot has a string variable $ S $ , which is initially an empty string. You can move the robot using the following four types of operations: - Operation $ 1 $ : Increase the robot's $ x $ coordinate by $ 1 $ and append `X` to the end of $ S $ . This operation costs $ 1 $ . - Operation $ 2 $ : Increase the robot's $ y $ coordinate by $ 1 $ and append `Y` to the end of $ S $ . This operation costs $ 1 $ . - Operation $ 3 $ : Decrease the robot's $ x $ coordinate by $ 1 $ and remove the last character of $ S $ . This operation can only be performed if the last character of $ S $ is `X`. This operation costs $ 0 $ . - Operation $ 4 $ : Decrease the robot's $ y $ coordinate by $ 1 $ and remove the last character of $ S $ . This operation can only be performed if the last character of $ S $ is `Y`. This operation costs $ 0 $ . Find the minimum cost required for the robot to visit all points $ 1, 2, \dots, N $ in this order.

The input is given from Standard Input in the following format: > $ N $ $ X_1 $ $ Y_1 $ $ X_2 $ $ Y_2 $ $ \vdots $ $ X_N $ $ Y_N $

Output the minimum cost required for the robot to visit all points in order.

### Sample Explanation 1 By performing Operation $ 1 $ once, Operation $ 2 $ three times, and Operation $ 1 $ twice, you can reach point $ 1 $ . Then, by performing Operation $ 3 $ twice and Operation $ 4 $ once, you can reach point $ 2 $ . The total cost of this sequence of operations is the sum of the number of times Operations $ 1 $ and $ 2 $ are performed, which is $ 6 $ . ### Constraints - All input values are integers. - $ 1 \le N \le 500 $ - $ 0 \le X_i, Y_i \le 10^9 $