<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) {
        vector<pair<int, int>> vp;
        map<int, int> all;
        for (auto& x : arrays) {
            vp.push_back({*x.begin(), *x.rbegin()});
            all[*x.begin()]++;
            all[*x.rbegin()]++;
        }
        int ans = -1;
        int n = arrays.size();
        for (auto& x : vp) {
            int first = x.first;
            int second = x.second;
            int first_far = all.rbegin()->first;
            if ((first_far != second) or
                (first_far == second and all[first_far] > 1)) {
                ans = max(ans, abs(first_far - first));
            } else {
                auto ptr = all.rbegin();
                ptr++;
                int first_far = ptr->first;
                ans = max(ans, abs(first_far - first));
            }
            int second_far = all.begin()->first;
            if ((second_far != first) or
                (second_far == first and all[second_far] > 1)) {
                ans = max(ans, abs(second_far - second));
            } else {
                auto ptr = all.begin();
                ptr++;
                int second_far = ptr->first;
                ans = max(ans, abs(second_far - second));
            }
        }

        return ans;
    }
};
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