<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) {
        int n = arrays.size();
        map<int,vector<int>> maxi;
        map<int, vector<int>> mini;


        int maxVal = arrays[0][0];
        int minVal = arrays[0][0];

        for(int i=0;i<n;i++){
            int m = arrays[i].size();
            mini[arrays[i][0]].push_back(i);
            if(arrays[i][0]<= minVal){
                minVal = arrays[i][0];
                
            }
            maxi[arrays[i][m-1]].push_back(i);
            if(arrays[i][m-1]>=maxVal){
                maxVal = arrays[i][m-1];
                
            }
        }
        cout<<"max: "<<maxVal<<" min: "<<minVal<<endl;
        for(auto it: maxi){
            cout<<it.first<<": ";
            for(auto i: it.second) cout<<i<<" ";
            cout<<endl;
        }
        cout<<"mini"<<endl;
        for(auto it: mini){
            cout<<it.first<<": ";
            for(auto i: it.second) cout<<i<<" ";
            cout<<endl;
        }
        if(maxi[maxVal].size()>1 or mini[minVal].size()>1 || maxi[maxVal][0]!= mini[minVal][0]) return maxVal - minVal;
        map<int, vector<int>>::iterator it = maxi.end();
        it--;
        it--;
        map<int, vector<int>>::iterator it1 = mini.begin();
        it1++;
        cout<<it->first<<" "<<it1->first<<endl;
        return max(abs(it->first-minVal), abs(it1->first-maxVal));

        

        
    }
};
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