<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) {
        auto last_elements = collectLast(arrays);
        int max_dis = 0;
        for (int i = 0 ; i < arrays.size(); i++) {
            int dis = findMax(last_elements, i) - arrays[i][0];
            if (dis > max_dis) {
                max_dis = dis;
            }
        }
        return max_dis;
    }

private:
   struct T {
     int v;
     int i; // index
   };

    // returns the max elements except elements[i].
    int findMax(const vector<T>& elements, int i) {
        int r = elements.size() - 1;
        return elements[r].i != i ? elements[r].v : elements[r - 1].v;
    }

    vector<T> collectLast(const vector<vector<int>>& arrays) {
        vector<T> last;
        for (int i = 0; i < arrays.size(); i++) {
            last.push_back(T{ *arrays[i].rbegin(), i });
        }
        std::sort(last.begin(), last.end(), [](const T& l, const T& r) {
            return l.v < r.v;
        });

        return last;
    }
};
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