There are several robots and factories located on the $X$ axis. You are given an integer array robot, where robot[i] represents the position of the $i^{ ext{th}}$ robot. You are also given a $2$D integer array factory, where factory[j] = [position$_j$, limit$_j$] indicates that the $j^{ ext{th}}$ factory is located at $ ext{position}_j$ and can repair at most $ ext{limit}_j$ robots.

Each robot must be assigned to a factory for repair such that no factory repairs more robots than its capacity limit. The distance a robot travels is the absolute difference between its initial position and the position of its assigned factory.

Return the minimum total distance traveled by all robots to repair every robot.

Note: The input is generated such that it is always possible to repair every robot.

Constraints:

• $1 \leq$ robot.length, factory.length $\leq 100$

• factory[j].length $= 2$

• $-10^9 \leq$ robot[i], $ ext{position}_j \leq 10^9$

• $0 \leq ext{limit}_j \leq$ robot.length

• The input will be generated such that it is always possible to repair every robot.

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