Denoting by $A$ the area of the largest resulting part of the division, the value of the land division tax is $A \times F$, where $F$ is the division tax factor set yearly by the County Council. Note that due to (2), in order to divide a piece of land into $N$ lots, $N - 1$ land divisions must be performed, and therefore $N - 1$ payments must be made to the County Council.
For example, considering the figure above, if the division tax factor is $2.5$ and the first land division separates the lot of $500$ units of area from the other lots, the land division tax to be paid for this first division is $2.5 \times (300 + 200 + 100 + 100 + 100)$. If the next land division separates the lot of $300$ units together with its neighbor lot of 100 units, from the set of the remaining lots, an additional $2.5 \times (300 + 100)$ must be paid in taxes, and so on. Note also that some land divisions are not possible, due to (2). For example, after the first land division mentioned above, it is not possible to make a land division to separate the lot of $300$ units together with the lot of $200$ units from the remaining three lots, because more than two parts would result from that operation.
Given the areas of all lots around the lake and the current value of the division tax factor, you must write a program to determine the smallest total land division tax that should be paid to divide the land according to the housing development plan.