<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 {
    string res;
    int digits[10] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, sum = 0;
public:
    void addMaxEqualLowerThan(int n) {
        for (int i = n; i >= 0; i--) if (digits[i]) {
            res.push_back(i + '0');
            digits[i]--;
            break;
        }
    }
    string largestTimeFromDigits(vector<int>& arr) {
        for (int i = 0; i < 4; i++) digits[arr[i]]++;
        for (int i = 0; i < 6; i++) {
            sum += digits[i];
            if (i == 2 && !sum || i == 3 && digits[2] && sum < 2 || i == 5 && sum < 2) return res;
        }
        if (digits[2] && sum > 2) {
            addMaxEqualLowerThan(2);
            addMaxEqualLowerThan(3);
            if (res == "2") {
                digits[2]++;
                res = "";
            }
        }
        if (!res.size()) {
            addMaxEqualLowerThan(1);
            addMaxEqualLowerThan(9);
        }
        res.push_back(':');
        addMaxEqualLowerThan(5);
        addMaxEqualLowerThan(9);
        return res.size() == 5 ? res : "";
    }
};
11000