<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 {
    map<pair<int, int>, int> m;
    int printHelper(string& s, int l, int r) {
        if (l > r)
            return 0;
        
        if (l == r)
            return 1;
        
        if (m.count(pair<int, int> (l, r)))
            return m[pair<int, int> (l, r)];
                
        if (s[l] == s[l+1]) {             
            m[pair<int, int> (l, r)] = printHelper(s, l+1, r);
            return m[pair<int, int> (l, r)];
        }
        
        int res = printHelper(s, l+1, r) + 1;
        for (int i = l+2; i <= r; i++) {
            if (s[i] == s[l]) {
                res = min(res, printHelper(s, l+1, i-1) + printHelper(s, i, r));
            }
        }
        m[pair<int, int> (l, r)] = res;
        return res;
    }
public:
    int strangePrinter(string s) {
        return printHelper(s, 0, s.size()-1);
    }
};
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