<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) {
        int max_val = -(int)1e9;
        int min_val = (int)1e9;
        
        int second_max, second_min;
        int idx;
        int i = 0;
        for (auto arr : arrays) {
            if (max_val < arr[arr.size() - 1]) {
                second_max = max_val;
                max_val = arr[arr.size() - 1];
                idx = i;
            } else if (second_max < arr[arr.size() - 1]) {
                second_max = arr[arr.size() - 1]; 
            }
            
            if (min_val > arr[0]) {
                second_min = min_val;
                min_val = arr[0];
            } else if (second_min > arr[0]) {
                second_min = arr[0];
            }
            i++;
        }    
        
        if (min_val == arrays[idx][0]) {
            return max(abs(max_val - second_min), abs(second_max - min_val));
        }
        return abs(max_val - min_val);
    }
};
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