I give a try to start at an O(mn) algorithm (where m is the size of the
longest bar)

Let Maxrect[i][j] denote the width of the maximum rectangle ending at the
ith position of height j

if(height[i] >= j)
Maxrect[i][j] = Maxrect[i-1][j]+1
else
Maxrect[i][j] = 0

We can traverse this array to find the maximum value in O(mn) now.
This may not be the best but to just get things rolling.

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