As you travel from Iraq towards IIT Guwahati, after a long time you find yourselves on a mountain trail in Tehran, Iran. The mountain trail is difficult and slippery. You suddenly get caught in a landslide and fall into a deep hole. Then the stones of 2 kg weight start falling onto you from above.
The hole is a 4x4 grid i.e., it is divided into 16 squares. Each square can accommodate only one stone (of any weight). To survive, you need at least one empty square. Owl notices your trouble and gives you the magical power to meld together stones, but only those of the same mass can be mould together. Since the stones are falling very fast, you are only able to push the stones in straight lines (horizontally/vertical- ly).
For example, when the arrangement of one of the rows in figure 1 when pushed horizontally to left trans- forms as shown:

If one stone falls every second, what is the maximum time for which you can survive i.e., when no square is empty and all stones become immovable?

Options

A. (2^16)-1
B. (2^17)-1
C. (2^17)-2
D. 2^16

Explanation

A
The maximum time for which you can survive is till the below situation occurs:
The time required for the above situation to occure is `(2+2^(2)+2^(3)+.....+2^(16))//2=2^(16)-1`