You need to sort the coins by weight, but this time you must use an unusual three way scale. The scale operates as follows:

- Three weights must be placed on the scale for a meaningful result.

- If all three weights are equal, the scale will be in perfect balance.

- If one weight is lighter than the other two, the scale will show that weight is the lightest.

- If two weights are equal and are lighter than the third, the scale will indicate that scenario.

Examples:

Ex1: If A=30 B=30 C=30 then the scale will be in balance.

Ex2: If A=30 B=31 C=32 then the scale will indicate that A is the lightest of the three, but not tell which of B and C is lighter.

Ex3: If A=30 B=31 C=31 then the scale will indicate that A is the lightest of the three, but not tell that B and C are equal. (undistinguishable from Ex2)

Ex4: If A=30 B=30 C=31 then the scale will indicate that A and B are equal and less than C.

Using this three way scale, can you sort the coins in five weighings?