<p>You have <code>n</code>&nbsp;&nbsp;<code>tiles</code>, where each tile has one letter <code>tiles[i]</code> printed on it.</p>

<p>Return <em>the number of possible non-empty sequences of letters</em> you can make using the letters printed on those <code>tiles</code>.</p>

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

<pre>
<strong>Input:</strong> tiles = &quot;AAB&quot;
<strong>Output:</strong> 8
<strong>Explanation: </strong>The possible sequences are &quot;A&quot;, &quot;B&quot;, &quot;AA&quot;, &quot;AB&quot;, &quot;BA&quot;, &quot;AAB&quot;, &quot;ABA&quot;, &quot;BAA&quot;.
</pre>

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

<pre>
<strong>Input:</strong> tiles = &quot;AAABBC&quot;
<strong>Output:</strong> 188
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> tiles = &quot;V&quot;
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= tiles.length &lt;= 7</code></li>
	<li><code>tiles</code> consists of uppercase English letters.</li>
</ul>

class Solution {
public:
    int numTilePossibilities(string tiles) {
        std::map<std::vector<int>, int> map = {};
        std::map<char, int> counts = {};
        std::vector<int> vec = {};
        for(char c = 'A'; c<='Z'; c++) {
            counts.insert({c, 0});
        }
        for(auto c:tiles) {
            counts[c]++;
        }
        for(int i = 0; i<26; i++) {
            vec.push_back(counts['A' + i]);
        }
        return helper(counts, map, vec);
    }

    int helper(std::map<char, int>& counts, std::map<std::vector<int>, int>& map, std::vector<int>& vec) {
        if(auto it = map.find(vec); it != map.end()){
            return map[vec];
        }
        map.insert({vec,0});
        for(int i = 0; i<26; i++) {
            if(counts['A' + i] > 0) {
                map[vec]++;
                counts['A' + i]--;
                vec[i]--;
                int help = helper(counts, map, vec);
                vec[i]++;
                map[vec] += help;
                counts['A' + i]++;
            }
        }
        return map[vec];
    }
};
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