<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 {
public:
    std::vector<int> mp;
    int n_;

    int get_key(int l, int r, char c) {
        if (c == ' ') c = 26;
        else c = c - 'a';
        return (int)(c) * n_ * n_ + l * n_ + r;
    }

    int solve(const string& s, int l, int r, char c) {
        if (l > r) return 0;
        if (l == r) return s[l] != c;

        if (s[l] == c) return solve(s, l + 1, r, c);
        if (s[r] == c) return solve(s, l, r - 1, c);

        // std::cout << l << " " << r << " " << c << std::endl;
        int key = get_key(l, r, c);
        // std::cout << key << std::endl;
        if (mp[key] != -1) return mp[key];
        int mn = 100;
        for (int i = l; i <= r; ++i) {
            mn = std::min(mn, 1 + solve(s, l + 1, i, s[l]) + solve(s, i + 1, r, c));
        }

        // std::cout << l << " " << r << " " << c << " " << mn << std::endl;
        mp[key] = mn;
        return mn;
    }

    int strangePrinter(string s) {
        n_ = s.size();
        mp.resize(n_ * n_ * 27 + 1, -1);
        // std::cout << mp.size() << std::endl;

        return solve(s, 0, s.size() - 1, ' ');
    }
};
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