The combination lock of this problem, as shown in the figure,
consists of a circular dial, which can be turned (clockwise or
counterclockwise) and is embedded into the "fixed" part of the
lock. The dial has `N` evenly spaced "ticks". The ticks
are numbered from 0 to `N`-1, increasing in the clockwise
direction. The fixed part of the lock has a "mark" which always
"points to" a particular tick on the dial. Of course, the mark
points to different ticks as the dial is turned. (In the figure,
`N` = 40 and the mark points to tick 14.)

The lock comes with three code numbers
`T`_{1},`T`_{2},
`T`_{3}. These are non-negative integers and each of
them is less than `N`. No two of the three are the
same.

The lock is opened in three stages of operations:

- If the mark initially points to tick
`T`_{1}, turn the dial exactly two full revolutions clockwise and stop. Otherwise, turn the dial clockwise exactly two full revolutions clockwise and continue to turn it clockwise until the mark points to tick`T`_{1}. - Turn the dial one full revolution counterclockwise and continue to
turn it counterclockwise until the mark points to tick
`T`_{2}. - Turn the dial clockwise until the mark points to tick
`T`_{3}. The lock should now open.

Given the numbers `N`, `T`_{1},
`T`_{2}, `T`_{3}, the goal of
this problem is to find the average number of ticks the dial must
be turned in order to open the lock. For any particular `N`,
`T`_{1}, `T`_{2},
`T`_{3} and a particular initial configuration of
the lock, the number of ticks turned is defined to be the sum of
the ticks turned in the three stages outlined above.

The input file consists of a number of test cases, one test case
per line. Each line of the input file contains four integers:
`N`, `T`_{1}, `T`_{2},
`T`_{3}, in this order, separated by blank
spaces. The integer `N` is a multiple of 5, 25 <=
`N` <= 100. The numbers `T`_{1},
`T`_{2} and `T`_{3} satisfy the
constraints stated under the description above. The input will
be terminated by a line containing only four zeroes, separated by blank
spaces.

For each test case, print the average number of ticks (rounded to
three decimal places) the dial must be turned in order to open the
lock. Assume that each of the `N` possible initial configurations of
the lock is equally likely.

80 20 40 50 80 10 79 12 0 0 0 0

369.500 415.500