<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:
    bool IsValid(string& s) {
      string hour = s.substr(0, 2);
      string minute = s.substr(3, 2);
      return hour >= "00" && hour <= "23" && minute >= "00" && minute <= "59";
    }
    string largestTimeFromDigits(vector<int>& arr) {
      vector<int> digit_count(10, 0);
      string res = "";
      for (int i = 0; i < 4; ++i) {
        for (int j = 0; j < 4; ++j) {
           if (j == i) continue;
           for (int k = 0; k < 4; ++k) {
            if (k == i || k == j) continue;
            for (int l = 0; l < 4; ++l) {
              if (l == i || l == j || l == k) continue;
              string s = to_string(arr[i]) + to_string(arr[j]) + ':' +
                         to_string(arr[k]) + to_string(arr[l]);
              if (IsValid(s)) {
                if (res.empty()) res = s;
                else if (s > res) res = s;
              }
            }
          }
        }
      }
      return res;
    }
};
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