<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 {
    int fact(int n) {
        int f = 1;
        for(int i=1; i<=n; i++) f *= i;
        return f;
    }
    void dfs(int i, string &t, string &s, unordered_set<string> &st) {
        if(i == t.size()) {
            string tmp = s;
            sort(tmp.begin(), tmp.end());
            st.insert(tmp);
            return;
        }
        dfs(i + 1, t, s, st);
        s += t[i];
        dfs(i + 1, t, s, st);
        s.pop_back();
    }
public:
    int numTilePossibilities(string tiles) {
        unordered_set<string> st;
        string s;
        int ans = 0;
        dfs(0, tiles, s, st);

        for(string str : st) {
            int n = fact(str.size());
            unordered_map<char, int> m;
            for(char c : str) m[c]++;
            for(auto i : m) n /= fact(i.second);
            ans += n;
        }
        return ans - 1; 
    }
};
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