<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)
    {
        static constexpr int s_cMinVal{-10'000};
        static constexpr int s_cMaxVal{10'000};
        static constexpr auto s_cInvalidIdx{std::numeric_limits<std::size_t>::max()};
        struct Info
        {
            int m_Val;
            std::size_t m_ArrIdx;
        };
        std::vector<Info> minValues; minValues.reserve(arrays.size());
        std::vector<Info> maxValues; maxValues.reserve(arrays.size());
        for (std::size_t idx{0}; idx != arrays.size(); ++idx)
        {
            minValues.emplace_back(arrays[idx].front(), idx);
            maxValues.emplace_back(arrays[idx].back(), idx);
        }
        std::ranges::sort(minValues, [](const auto lhs, const auto rhs) { return lhs.m_Val < rhs.m_Val; });
        std::ranges::sort(maxValues, [](const auto lhs, const auto rhs) { return lhs.m_Val > rhs.m_Val; });

        if (minValues.front().m_ArrIdx == maxValues.front().m_ArrIdx)
        {
            return std::max(
                std::abs(minValues[1].m_Val - maxValues[0].m_Val),
                std::abs(minValues[0].m_Val - maxValues[1].m_Val));
        }

        return std::abs(minValues[0].m_Val - maxValues[0].m_Val);
    }
};
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