<p>There is a strange printer with the following two special properties:</p>

<ul>
	<li>The printer can only print a sequence of <strong>the same character</strong> each time.</li>
	<li>At each turn, the printer can print new characters starting from and ending at any place and will cover the original existing characters.</li>
</ul>

<p>Given a string <code>s</code>, return <em>the minimum number of turns the printer needed to print it</em>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;aaabbb&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> Print &quot;aaa&quot; first and then print &quot;bbb&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;aba&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> Print &quot;aaa&quot; first and then print &quot;b&quot; from the second place of the string, which will cover the existing character &#39;a&#39;.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 100</code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution:
    def strangePrinter(self, s: str) -> int:
        reduced_s = s[0]
        for i in range(1, len(s)):
            if s[i] != reduced_s[-1]:
                reduced_s = reduced_s + s[i]
        @cache
        def strangeReduced(reduced, base_char=' '):
            if all(r == base_char for r in reduced):
                return 0
            if reduced[0] == base_char:
                reduced = reduced[1:]
            if reduced[-1] == base_char:
                reduced = reduced[:-1]
            running_best = float('inf')
            indices = defaultdict(list)
            for i, c in enumerate(reduced):
                indices[c].append(i)
            c_indices = indices[reduced[0]]
            c = reduced[0]
            start = 0
            for stop in c_indices:
                # What if we printed from start to stop?
                cost = strangeReduced(reduced[:start], base_char) + strangeReduced(reduced[stop+1:], base_char) + strangeReduced(reduced[start+1: stop], c)
                if c != base_char:
                    cost += 1
                running_best = min(cost, running_best)
            return running_best
        return strangeReduced(reduced_s)



20900