<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(object):
    def isSolvable(self, words, result):
        words.append(result)
        R, C = len(words), max(map(len, words))

        assigned = {}
        assigned_inv = [None] * 10

        def search(column, row, bal):
            if column >= C:
                return bal == 0
            if row == R:
                return bal % 10 == 0 and search(column + 1, 0, bal // 10)

            word = words[row]
            if column >= len(word):
                return search(column, row + 1, bal)

            letter = word[~column]
            sign = 1 if row < R - 1 else -1
            if letter in assigned:
                if (assigned[letter] or len(word) == 1 or column != len(word) - 1):
                    return search(column, row + 1, bal + sign * assigned[letter])
                return False
            else:
                for d, ad in enumerate(assigned_inv):
                    if ad is None and (d or len(word) == 1 or column != len(word) - 1):
                        assigned_inv[d] = letter
                        assigned[letter] = d
                        if search(column, row + 1, bal + sign * d):
                            return True
                        assigned_inv[d] = None
                        del assigned[letter]

            return False

        return search(0, 0, 0)
16600