<p>Given an equation, represented by <code>words</code> on the left side and the <code>result</code> on the right side.</p>

<p>You need to check if the equation is solvable under the following rules:</p>

<ul>
	<li>Each character is decoded as one digit (0 - 9).</li>
	<li>No two characters can map to the same digit.</li>
	<li>Each <code>words[i]</code> and <code>result</code> are decoded as one number <strong>without</strong> leading zeros.</li>
	<li>Sum of numbers on the left side (<code>words</code>) will equal to the number on the right side (<code>result</code>).</li>
</ul>

<p>Return <code>true</code> <em>if the equation is solvable, otherwise return</em> <code>false</code>.</p>

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

<pre>
<strong>Input:</strong> words = [&quot;SEND&quot;,&quot;MORE&quot;], result = &quot;MONEY&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> Map &#39;S&#39;-&gt; 9, &#39;E&#39;-&gt;5, &#39;N&#39;-&gt;6, &#39;D&#39;-&gt;7, &#39;M&#39;-&gt;1, &#39;O&#39;-&gt;0, &#39;R&#39;-&gt;8, &#39;Y&#39;-&gt;&#39;2&#39;
Such that: &quot;SEND&quot; + &quot;MORE&quot; = &quot;MONEY&quot; ,  9567 + 1085 = 10652</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;SIX&quot;,&quot;SEVEN&quot;,&quot;SEVEN&quot;], result = &quot;TWENTY&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> Map &#39;S&#39;-&gt; 6, &#39;I&#39;-&gt;5, &#39;X&#39;-&gt;0, &#39;E&#39;-&gt;8, &#39;V&#39;-&gt;7, &#39;N&#39;-&gt;2, &#39;T&#39;-&gt;1, &#39;W&#39;-&gt;&#39;3&#39;, &#39;Y&#39;-&gt;4
Such that: &quot;SIX&quot; + &quot;SEVEN&quot; + &quot;SEVEN&quot; = &quot;TWENTY&quot; ,  650 + 68782 + 68782 = 138214</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;LEET&quot;,&quot;CODE&quot;], result = &quot;POINT&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> There is no possible mapping to satisfy the equation, so we return false.
Note that two different characters cannot map to the same digit.
</pre>

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

<ul>
	<li><code>2 &lt;= words.length &lt;= 5</code></li>
	<li><code>1 &lt;= words[i].length, result.length &lt;= 7</code></li>
	<li><code>words[i], result</code> contain only uppercase English letters.</li>
	<li>The number of different characters used in the expression is at most <code>10</code>.</li>
</ul>


class Solution:
    def isSolvable(self, words: List[str], result: str) -> bool:
        start = set()
        for word in words + [result]:
            if len(word) > 1:
                start.add(word[0])


        n = max(map(len, words + [result]))
        if len(result) < n:
            return False

        def dfs(idx, i, carry, visited, mp):
            if idx == n:
                return carry == 0
            if i == len(words) + 1:
                sums = sum(mp[word[-idx - 1]] if idx < len(word) else 0 for word in words) + carry
                if sums % 10 == mp[result[-idx - 1]]:
                    carry = sums // 10
                    return dfs(idx + 1, 0, carry, visited, mp)
                return False

            if (i < len(words) and idx >= len(words[i])):
                return dfs(idx, i + 1, carry, visited, mp)
            tmp = words + [result]
            ch = tmp[i][-idx-1]
            if ch in mp:
                return dfs(idx, i + 1, carry, visited, mp)
            begin = 0
            if ch in start:
                begin = 1
            for x in range(begin, 10):
                if x not in visited:
                    visited.add(x)
                    mp[ch] = x
                    if dfs(idx, i + 1, carry, visited, mp.copy()):
                        return True
                    visited.remove(x)
            return False

        return dfs(0, 0, 0, set(), {})
16700