Minimum Distance to Type a Word Using Two Fingers
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/02/leetcode_keyboard.png" style="width: 349px; height: 209px;" />
<p>You have a keyboard layout as shown above in the <strong>X-Y</strong> plane, where each English uppercase letter is located at some coordinate.</p>

<ul>
	<li>For example, the letter <code>&#39;A&#39;</code> is located at coordinate <code>(0, 0)</code>, the letter <code>&#39;B&#39;</code> is located at coordinate <code>(0, 1)</code>, the letter <code>&#39;P&#39;</code> is located at coordinate <code>(2, 3)</code> and the letter <code>&#39;Z&#39;</code> is located at coordinate <code>(4, 1)</code>.</li>
</ul>

<p>Given the string <code>word</code>, return <em>the minimum total <strong>distance</strong> to type such string using only two fingers</em>.</p>

<p>The <strong>distance</strong> between coordinates <code>(x<sub>1</sub>, y<sub>1</sub>)</code> and <code>(x<sub>2</sub>, y<sub>2</sub>)</code> is <code>|x<sub>1</sub> - x<sub>2</sub>| + |y<sub>1</sub> - y<sub>2</sub>|</code>.</p>

<p><strong>Note</strong> that the initial positions of your two fingers are considered free so do not count towards your total distance, also your two fingers do not have to start at the first letter or the first two letters.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> word = &quot;CAKE&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> Using two fingers, one optimal way to type &quot;CAKE&quot; is: 
Finger 1 on letter &#39;C&#39; -&gt; cost = 0 
Finger 1 on letter &#39;A&#39; -&gt; cost = Distance from letter &#39;C&#39; to letter &#39;A&#39; = 2 
Finger 2 on letter &#39;K&#39; -&gt; cost = 0 
Finger 2 on letter &#39;E&#39; -&gt; cost = Distance from letter &#39;K&#39; to letter &#39;E&#39; = 1 
Total distance = 3
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> word = &quot;HAPPY&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> Using two fingers, one optimal way to type &quot;HAPPY&quot; is:
Finger 1 on letter &#39;H&#39; -&gt; cost = 0
Finger 1 on letter &#39;A&#39; -&gt; cost = Distance from letter &#39;H&#39; to letter &#39;A&#39; = 2
Finger 2 on letter &#39;P&#39; -&gt; cost = 0
Finger 2 on letter &#39;P&#39; -&gt; cost = Distance from letter &#39;P&#39; to letter &#39;P&#39; = 0
Finger 1 on letter &#39;Y&#39; -&gt; cost = Distance from letter &#39;A&#39; to letter &#39;Y&#39; = 4
Total distance = 6
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= word.length &lt;= 300</code></li>
	<li><code>word</code> consists of uppercase English letters.</li>
</ul>

['minimum-time-to-type-word-using-special-typewriter']
[]
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{
  "name": "minimumDistance",
  "params": [
    {
      "name": "word",
      "type": "string"
    }
  ],
  "return": {
    "type": "integer"
  }
}
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Using compile arguments: <code>--enable-preview --release 21</code></p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>"], "python": ["Python", "<p><code>Python 2.7.18</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/2/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/2/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/2/library/collections.html\" target=\"_blank\">collections</a>. 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Your code will be compiled with <code>opt-level</code> 2.</p>\r\n\r\n<p>Supports <a href=\"https://crates.io/crates/rand\" target=\"_blank\">rand v0.8</a> and <a href=\"https://crates.io/crates/regex\" target=\"_blank\">regex\u00a0v1</a> and <a href=\"https://crates.io/crates/itertools\" target=\"_blank\">itertools\u00a0v0.14</a> from crates.io</p>"], "php": ["PHP", "<p><code>PHP 8.2</code>.</p>\r\n<p>With bcmath module</p>"], "typescript": ["Typescript", "<p><code>TypeScript 5.7.3, Node.js 22.14.0</code>.</p>\r\n\r\n<p>Compile Options: <code>--alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2024</code></p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "racket": ["Racket", "<p><a href=\"https://docs.racket-lang.org/guide/performance.html#%28tech._c%29\" target=\"_blank\">Racket CS</a> v8.15</p>\r\n\r\n<p>Using <code>#lang racket</code></p>\r\n\r\n<p>Required <code>data/gvector data/queue data/order data/heap</code> automatically for your convenience</p>"], "erlang": ["Erlang", "Erlang/OTP 26"], "elixir": ["Elixir", "Elixir 1.17 with Erlang/OTP 26"], "dart": ["Dart", "<p>Dart 3.2. 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['String', 'Dynamic Programming']