<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:
        var = {}
        digits = set()
        
        def check(column, carry):
            s = sum((var[w[-1-column]] for w in words if len(w) > column)) + carry
            c = result[-1-column]
            if c in var:
                if var[c] != s % 10:
                    return -1, False
                else:
                    return s // 10, False
            if s % 10 == 0 and c in leadings:
                return -1, False
            if s % 10 in digits:
                return -1, False
            var[c] = s % 10
            digits.add(s % 10)
            return s // 10, c

        def dfs(column, word_id, carry):
            reset = False
            if word_id >= len(words):
                carry, reset = check(column, carry)
                if carry < 0:
                    return False
                word_id = 0
                column += 1
            if column >= len(result):
                if carry == 0:
                    return True
            elif len(words[word_id]) <= column or words[word_id][-1-column] in var:
                if dfs(column, word_id+1, carry):
                    return True
            else:
                c = words[word_id][-1-column]
                for d in range(10):
                    if (d in digits) or (d == 0 and c in leadings):
                        continue
                    digits.add(d)
                    var[c] = d
                    if dfs(column, word_id+1, carry):
                        return True
                    digits.remove(d)
                    del var[c]
            if reset != False:
                digits.remove(var[reset])
                del var[reset]
            return False

        leadings = set([w[0] for w in words + [result] if len(w) > 1])
        if any(len(w) > len(result) for w in words):
            return False
        return dfs(0, 0, 0)
16800