- initially, the n balls, numbered from 1 to n, are located in area A, in random order;
- by pressing button I the first ball from area A falls in area B;
- by pressing button O the first ball from area B goes up to area C.
Task
Because the honorable scientist hopes to sell his invention to a lottery, help him by writing a program that indicates the order in which the two buttons have to be pressed so that starting from an initial ball configuration in area A we can get a specific configuration of the balls in area C (which will prove the extraordinary importance of the machine!).
Input Data
Input file bile.in
has the following structure:
Output Data
Output file bile.out will contain a single line with a sequence comprised of letters I and O representing the order in which the two buttons have to be pressed so that starting from the initial configuration we get the final configuration or message imposibil if it cannot be achieved.
Constraints