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

• $1\le n,m\le 100000$,
• $0\le r[i]\le {10}^9($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 $1$: $nm$
• 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.