<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 {
public:
    string largestTimeFromDigits(vector<int>& arr) {
        //just try all four
        vector<string> times;
        for(int i=0; i<arr.size(); i++){
            for(int j=1; j<=3; j++){
                for(int k=1; k<=3; k++){
                    if((k+i)%arr.size() == (j+i)%arr.size())
                        continue;
                    for(int l=1; l<=3; l++){
                         if((k+i)%arr.size() == (l+i)%arr.size()||(j+i)%arr.size() == (l+i)%arr.size())
                            continue;
                        times.push_back(to_string(arr[i])+to_string(arr[(i+j)%arr.size()])+':'
                        +to_string(arr[(i+k)%arr.size()]) +to_string(arr[(i+l)%arr.size()]));
                    }
                }
            }
        }
        // for(string s : times)
        //     cout << s << endl;
        sort(times.rbegin(), times.rend());
        //check validity
        for(string s : times){
            if(stoi(s.substr(0,2))<=23 && stoi(s.substr(3,2))<=59)
                return s;
            // cout <<s << " ";
        }
        return "";
        
        
    }
};
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