<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>> v;
        for(int m = 0; m < arrays.size(); ++m){
            //for(auto a: arrays[m]) v.push_back({a, m});
            v.push_back({arrays[m][0], m});
            v.push_back({arrays[m][arrays[m].size()-1], m});
        }
        sort(v.begin(), v.end());
        //for(auto a: v) cout<<a.first<<" "<<a.second<<endl;cout<<endl;
        int lo = 0, hi = v.size() - 1;
        while(lo < hi){
            //cout<<v[lo].first<<" "<<v[hi].first<<endl;
            if(v[lo].second != v[hi].second) return v[hi].first - v[lo].first;
            if(v[lo+1].first - v[lo].first < v[hi].first - v[hi-1].first){
                ++lo;
            } else if(v[lo+1].first - v[lo].first > v[hi].first - v[hi-1].first){
                --hi;
            } else{
                if(v[lo+1].second != v[lo].second) ++lo;
                else if(v[hi].second != v[hi-1].second) --hi;
                else ++lo, --hi;
            }
        }
        return 0;
    }
};
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