<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:

    int Dp(int l, int r, vector<vector<int>>& dp, vector<vector<int>>& pos, char fill, string& s){
        
        if(l > r)   return 0;
        if(l == r)  return (s[l] == fill)? 0 : 1;

        if(dp[l][r] != INT_MAX) return dp[l][r];
        if(s[l] == fill)    return Dp(l + 1, r, dp, pos, fill, s);
         
        char c =  s[l] - 'a';
        int idx = lower_bound(pos[c].begin(), pos[c].end(), l) - pos[c].begin();
        for(;idx < pos[c].size(); idx++){
            dp[l][r] = min(dp[l][r], 1 + Dp(l + 1, pos[c][idx] - 1, dp, pos, c + 'a', s) + Dp(pos[c][idx] + 1, r, dp, pos, fill, s));
        } 

        return dp[l][r];
        
    }

    int strangePrinter(string s) {
        
        vector<vector<int>> pos(26);
        for(int i = 0; i < s.size(); i++){
            pos[s[i] - 'a'].push_back(i);
        }

        vector<vector<int>> dp(s.size(), vector<int>(s.size(), INT_MAX));
        return Dp(0, s.size() - 1, dp, pos, ' ', s);

    }
};
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