<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) {
        // 2 2 6 6
        // 1 6 6 6
        // 2 6 2 6
        // if there is only two nums less than 6, then have to use one of thme in the mins 
        vector <int> free(11);
        int six = 0;
        for (auto i :arr) {
            free[i]++;
            if (i<6)six++;
        }
        vector <int > ans;
        int mx[4] = {2,9,5,9};
        if (six==2) mx[0]=1;
        for (int x=0;x<4;x++){
            int i = mx[x];
            while (i>=0){
                if (free[i]>0){
                    free[i]--;
                    ans.push_back(i);
                    break;
                }
                i--;
            }
            if (ans.size()<x+1) return "";
            if (x==0&&ans[0]==2) mx[1]=3;
        }
        string sans;
        int c = 0;
        for (auto i : ans) {
            sans+=(to_string(i));
            c++;
            if (c==2) sans+=":";
        }
        return sans;
    }
};
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