<p>Given an array <code>arr</code> of 4 digits, find the latest 24-hour time that can be made using each digit <strong>exactly once</strong>.</p>

<p>24-hour times are formatted as <code>&quot;HH:MM&quot;</code>, where <code>HH</code> is between <code>00</code> and <code>23</code>, and <code>MM</code> is between <code>00</code> and <code>59</code>. The earliest 24-hour time is <code>00:00</code>, and the latest is <code>23:59</code>.</p>

<p>Return <em>the latest 24-hour time in <code>&quot;HH:MM&quot;</code> format</em>. If no valid time can be made, return an empty string.</p>

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

<pre>
<strong>Input:</strong> arr = [1,2,3,4]
<strong>Output:</strong> &quot;23:41&quot;
<strong>Explanation:</strong> The valid 24-hour times are &quot;12:34&quot;, &quot;12:43&quot;, &quot;13:24&quot;, &quot;13:42&quot;, &quot;14:23&quot;, &quot;14:32&quot;, &quot;21:34&quot;, &quot;21:43&quot;, &quot;23:14&quot;, and &quot;23:41&quot;. Of these times, &quot;23:41&quot; is the latest.
</pre>

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

<pre>
<strong>Input:</strong> arr = [5,5,5,5]
<strong>Output:</strong> &quot;&quot;
<strong>Explanation:</strong> There are no valid 24-hour times as &quot;55:55&quot; is not valid.
</pre>

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

<ul>
	<li><code>arr.length == 4</code></li>
	<li><code>0 &lt;= arr[i] &lt;= 9</code></li>
</ul>

class Solution:
    def largestTimeFromDigits(self, arr: List[int]) -> str:
        arr.sort()

        def construct(used, result):
            # print(result)
            if len(result) == 4:
                return result

            index = len(result)
            for i in range(3, -1, -1):
                if i in used:
                    continue 

                val = arr[i]

                if index == 0 and val > 2:
                    continue
                
                if index == 1 and result[0] == '2' and val > 3:
                    continue
                
                if index == 2 and val > 5:
                    continue
                
                result.append(str(val))
                used.add(i)
                attempt = construct(used, result)
                used.remove(i)
                if attempt is not None:
                    return attempt

                del result[len(result) - 1]
            
            return None
        

        result = construct(set(), [])
        if result is None:
            return ""
        
        return "".join(result[0:2]) + ':' + "".join(result[2:4])

            



        





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