<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:
        ps = s[0]
        for char in s:
            if char != ps[-1]:
                ps+=char
        dp_table = {}
        def Minimun(start,end):
            if start > end:
                return 0
            
            if (start,end) in dp_table:
                return dp_table[(start,end)]
            
            the_min = 1 + Minimun(start+1,end)

            for k in range(start + 1, end+1):
                if ps[k] == ps[start]:
                    temp_min = Minimun(start,k-1) + Minimun(k+1,end)
                    the_min = min(the_min,temp_min)

            dp_table[(start,end)] = the_min
            return the_min
        return Minimun(0,len(ps)-1)


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