<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:
    def numTilePossibilities(self, tiles: str) -> int:
        if len(tiles) == 1:
            return 1
        # class Solution:
    # def numTilePossibilities(self, tiles: str) -> int:
        record = [0] * 26
        for tile in tiles: record[ord(tile)-ord('A')] += 1
        def dfs(record):
            s = 0
            for i in range(26):
                if not record[i]: continue
                record[i] -= 1
                s += dfs(record) + 1 
                record[i] += 1
            return s    
        return dfs(record)

        # def dfs(i, e):
        #     nonlocal tiles
        #     nonlocal c
        #     if i >= len(tiles):
        #         return

        #     cc = tiles[i]
            
        #     e.append(cc)
        #     c.append(''.join(e))
        #     dfs(i+1, e)
        #     e.pop()
        #     dfs(i+1, e)
        #     c.append(''.join(e))

        # dfs(0, [])
        # ss = 0
        # for i in range(1, len(tiles)+1):
        #     ss += len(list(combinations(tiles, i)))
        # print(ss)

        # return ss+1
16300