As a collector of rare coins, you have a special cabinet with sixteen numbered
compartments (as shown below). Each compartment contains the same number of coins as
what is shown on the label. At least it did, until somebody mixed up your coins, so
that __no compartment holds the same number of coins as what is shown on the label__
(although each compartment does still hold a different number of coins from one
to sixteen).

Can you figure out, from the following clues, the new arrangement? (Note that "directly" means contiguous or touching.)

- The compartment with three coins now lies directly above the compartment which now has sixteen coins.
- The new number of coins in one compartment is the square of the old number, and it is directly above a compartment with twice as many coins in it now than it used to have.
- The compartment which now has two coins is not in the left-most column.
- One of the compartments now has half as many coins as it had before. It is directly below a compartment which now has twice as many coins as before, and dircetly above a compartment which has one less coin than before.
- The compartment which now holds thirteen coins lies directly to the right of the compartment which now holds fifteen coins.
- Following one of the two diagonals: one compartment now has nine less coins, the next has ten less, the next has twice as many as it started with, the last has nine more.
- The compartment now containing six coins lies directly below the compartment which used to contain six coins.