<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) {
        std::deque<std::tuple<int, int>> mins;
        std::deque<std::tuple<int, int>> maxes;

        for (int i = 0; i < arrays.size(); i++) {
            std::tuple<int, int> minItem = {arrays[i][0], i};
            auto minIt = std::lower_bound(mins.begin(), mins.end(), minItem);
            mins.insert(minIt, minItem);
            if (mins.size() > 2)
                mins.pop_back();

            std::tuple<int, int> maxItem = {arrays[i][arrays[i].size()-1], i};
            auto maxIt = std::lower_bound(maxes.begin(), maxes.end(), maxItem);
            maxes.insert(maxIt, maxItem);
            
            if (maxes.size() > 2)
                maxes.pop_front();
        }

        auto min = mins.front();
        auto max = maxes.back();
        if (std::get<1>(min) != std::get<1>(max)) {
            return std::get<0>(max) - std::get<0>(min);
        }

        auto otherMin = mins.back();
        auto otherMax = maxes.front();

        if (std::get<0>(max) - std::get<0>(otherMin) > std::get<0>(otherMax) - std::get<0>(min)) {
            return std::get<0>(max) - std::get<0>(otherMin);
        } else {
            return std::get<0>(otherMax) - std::get<0>(min);
        }
    }
};
119213