<p>You are given a <strong>0-indexed</strong> binary string <code>s</code> which represents a sequence of train cars. <code>s[i] = '0'</code> denotes that the <code>i<sup>th</sup></code> car does <strong>not</strong> contain illegal goods and <code>s[i] = '1'</code> denotes that the <code>i<sup>th</sup></code> car does contain illegal goods.</p> <p>As the train conductor, you would like to get rid of all the cars containing illegal goods. You can do any of the following three operations <strong>any</strong> number of times:</p> <ol> <li>Remove a train car from the <strong>left</strong> end (i.e., remove <code>s[0]</code>) which takes 1 unit of time.</li> <li>Remove a train car from the <strong>right</strong> end (i.e., remove <code>s[s.length - 1]</code>) which takes 1 unit of time.</li> <li>Remove a train car from <strong>anywhere</strong> in the sequence which takes 2 units of time.</li> </ol> <p>Return <em>the <strong>minimum</strong> time to remove all the cars containing illegal goods</em>.</p> <p>Note that an empty sequence of cars is considered to have no cars containing illegal goods.</p> <p> </p> <p><strong>Example 1:</strong></p> <pre> <strong>Input:</strong> s = "<strong><u>11</u></strong>00<strong><u>1</u></strong>0<strong><u>1</u></strong>" <strong>Output:</strong> 5 <strong>Explanation:</strong> One way to remove all the cars containing illegal goods from the sequence is to - remove a car from the left end 2 times. Time taken is 2 * 1 = 2. - remove a car from the right end. Time taken is 1. - remove the car containing illegal goods found in the middle. Time taken is 2. This obtains a total time of 2 + 1 + 2 = 5. An alternative way is to - remove a car from the left end 2 times. Time taken is 2 * 1 = 2. - remove a car from the right end 3 times. Time taken is 3 * 1 = 3. This also obtains a total time of 2 + 3 = 5. 5 is the minimum time taken to remove all the cars containing illegal goods. There are no other ways to remove them with less time. </pre> <p><strong>Example 2:</strong></p> <pre> <strong>Input:</strong> s = "00<strong><u>1</u></strong>0" <strong>Output:</strong> 2 <strong>Explanation:</strong> One way to remove all the cars containing illegal goods from the sequence is to - remove a car from the left end 3 times. Time taken is 3 * 1 = 3. This obtains a total time of 3. Another way to remove all the cars containing illegal goods from the sequence is to - remove the car containing illegal goods found in the middle. Time taken is 2. This obtains a total time of 2. Another way to remove all the cars containing illegal goods from the sequence is to - remove a car from the right end 2 times. Time taken is 2 * 1 = 2. This obtains a total time of 2. 2 is the minimum time taken to remove all the cars containing illegal goods. There are no other ways to remove them with less time.</pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= s.length <= 2 * 10<sup>5</sup></code></li> <li><code>s[i]</code> is either <code>'0'</code> or <code>'1'</code>.</li> </ul>