In the first line, print a single integer $k$~--- the number of button presses in your solution ($1 \le k \le 1000$).

In the second line, print the applied operations in order, separated by spaces.

The solution will be checked with a program in C++ using the standard 64-bit floating-point type: \t{double}. Your answer will be considered correct if the sequence of actions does not cause an error, and in the end the calculator displays $\frac {a}{b}$ with an absolute error of at most $10^{-9}$.

You do not have to find the shortest solution. Any solution satisfying the constraints will be accepted.