<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>>& arr){
        // smallest of the first index 
        // largest of the last index if not picked 

        // you have to pick from different arrays 
        
        int n = (int)arr.size(); 

        vector<pair<int, int>> v(n); 

        long long result = 0; 

        stack<long long> st1; 
        st1.push(INT_MAX); 
        stack<long long> st2; 
        st2.push(INT_MIN); 

        for(int i = n-1; i >= 0; i--) {
            int m = (int)arr[i].size(); 

            // check for the element in the max 
            result = max({result, st2.top() - arr[i][0], arr[i][m-1] - st1.top()}); 
            
            if (st1.top() > arr[i][0]) {
                st1.push(arr[i][0]); 
            }

            if (st2.top() < arr[i][m-1]) {
                st2.push(arr[i][m-1]); 
            }
        }

        return result; 
    }
};
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