Maryam is an electrical engineer. She is designing wiring on a communication tower. On the tower there are some connection points, placed at distinct heights. A wire can be used to connect any two connection points. Each connection point can be connected to an arbitrary number of wires. There are two types of connection points: red and blue.

For the purpose of this problem the tower should be viewed as a line and the connection points as blue and red points that are at non-negative integer coordinates on this line. The length of a wire is the distance between the two connection points it connects.

Your goal is to help Maryam find a wiring scheme such that:

1. Each connection point has at least one wire to a connection point of a different color.
2. The total length of the wires is minimized.

Implementation details

You should implement the following procedure:

long long min_total_length(std::vector<int> r, std::vector<int> b)

• ~r~: array of length ~n~ containing the positions of the red connection points in increasing order.
• ~b~: array of length ~m~ containing the positions of the blue connection points in increasing order.
• This procedure should return the minimum total length of wires, among all valid wiring schemes.
• Note that the return type of this procedure is long long.

Example

min_total_length({1, 2, 3, 7}, {0, 4, 5, 9, 10})

The figure below illustrates this example.

• The tower is shown horizontally.
• In the black-and-white printed version of the problem statement the red connection points are dark and the blue ones are light.
• There are ~4~ red connection points, located at positions ~1~, ~2~, ~3~, and ~7~.
• There are ~5~ blue connection points, located at positions ~0~, ~4~, ~5~, ~9~, and ~10~.
• One optimal solution is shown in the figure above.
• In this solution, the total length of the wires is ~1 + 2 + 2 + 2 + 3 = 10~, which is optimal. So, the procedure should return ~10~.
• Note that two wires are connected to the connection point at position ~7~.

Constraints

• ~1 \le n,m \le 100\,000~,
• ~0 \le r[i] \le 10^9 (~for all ~0 \le i \le n-1)~,
• ~0 \le b[i] \le 10^9 (~for all ~0 \le i \le m-1)~,
• Each of the arrays ~r~ and ~b~ is sorted in ascending order.
• All ~n + m~ values in the arrays ~r~ and ~b~ are distinct.

Subtasks

1. (7 points) ~n,m \le 200~,
2. (13 points) All red connection points have positions smaller than any blue connection points.
3. (10 points) There is at least one red connection point and one blue connection point among every ~7~ consecutive connection points.
4. (25 points) All connection points have different positions in the range ~[1, n+m]~.
5. (45 points) No additional constraints.

Sample grader

The sample grader reads the input in the following format:

• line ~1~: ~n\ m~
• line ~2~: ~r[0]\ r[1]\ \dots\ r[n-1]~
• line ~3~: ~b[0]\ b[1]\ \dots\ b[m-1]~

The sample grader prints a single line containing the return value of min_total_length.