<p>There are some robots and factories on the X-axis. You are given an integer array <code>robot</code> where <code>robot[i]</code> is the position of the <code>i<sup>th</sup></code> robot. You are also given a 2D integer array <code>factory</code> where <code>factory[j] = [position<sub>j</sub>, limit<sub>j</sub>]</code> indicates that <code>position<sub>j</sub></code> is the position of the <code>j<sup>th</sup></code> factory and that the <code>j<sup>th</sup></code> factory can repair at most <code>limit<sub>j</sub></code> robots.</p>
<p>The positions of each robot are <strong>unique</strong>. The positions of each factory are also <strong>unique</strong>. Note that a robot can be <strong>in the same position</strong> as a factory initially.</p>
<p>All the robots are initially broken; they keep moving in one direction. The direction could be the negative or the positive direction of the X-axis. When a robot reaches a factory that did not reach its limit, the factory repairs the robot, and it stops moving.</p>
<p><strong>At any moment</strong>, you can set the initial direction of moving for <strong>some</strong> robot. Your target is to minimize the total distance traveled by all the robots.</p>
<p>Return <em>the minimum total distance traveled by all the robots</em>. The test cases are generated such that all the robots can be repaired.</p>
<p><strong>Note that</strong></p>
<ul>
<li>All robots move at the same speed.</li>
<li>If two robots move in the same direction, they will never collide.</li>
<li>If two robots move in opposite directions and they meet at some point, they do not collide. They cross each other.</li>
<li>If a robot passes by a factory that reached its limits, it crosses it as if it does not exist.</li>
<li>If the robot moved from a position <code>x</code> to a position <code>y</code>, the distance it moved is <code>|y - x|</code>.</li>
