<p>You are given <code>m</code> <code>arrays</code>, where each array is sorted in <strong>ascending order</strong>.</p>

<p>You can pick up two integers from two different arrays (each array picks one) and calculate the distance. We define the distance between two integers <code>a</code> and <code>b</code> to be their absolute difference <code>|a - b|</code>.</p>

<p>Return <em>the maximum distance</em>.</p>

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

<pre>
<strong>Input:</strong> arrays = [[1,2,3],[4,5],[1,2,3]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> One way to reach the maximum distance 4 is to pick 1 in the first or third array and pick 5 in the second array.
</pre>

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

<pre>
<strong>Input:</strong> arrays = [[1],[1]]
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>m == arrays.length</code></li>
	<li><code>2 &lt;= m &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= arrays[i].length &lt;= 500</code></li>
	<li><code>-10<sup>4</sup> &lt;= arrays[i][j] &lt;= 10<sup>4</sup></code></li>
	<li><code>arrays[i]</code> is sorted in <strong>ascending order</strong>.</li>
	<li>There will be at most <code>10<sup>5</sup></code> integers in all the arrays.</li>
</ul>

class Solution {
public:
    int maxDistance(vector<vector<int>>& arrays) {
        priority_queue<vector<int>, vector<vector<int>>> pq;
        for(int i=0; i < arrays.size(); i++) {
            if(pq.size() < 2) {
                pq.push({arrays[i][0],i});
            } else if(pq.top()[0] > arrays[i][0]) {
                pq.pop();
                pq.push({arrays[i][0],i});
            }
        }
        
        priority_queue<vector<int>, vector<vector<int>>, greater<>> mpq;
        for(int i=0; i < arrays.size(); i++) {
            if(mpq.size() < 2) {
                mpq.push({arrays[i].back(),i});
            } else if(mpq.top()[0] < arrays[i].back()) {
                mpq.pop();
                mpq.push({arrays[i].back(),i});
            }
        }

        auto l1 = pq.top();
        pq.pop();
        auto l2 = pq.top();

        auto h1 = mpq.top();
        mpq.pop();
        auto h2 = mpq.top();
        cout<<h1[0]<<" "<<h2[0]<<" "<<l1[0]<<" "<<l2[0]<<endl;
        if(h2[1] != l2[1])
            return h2[0] - l2[0];
        return max(h2[0]-l1[0], h1[0]-l2[0]);
    }
};
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