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In modern gadgets, it's crucial to trim down the fat and get rid of unnecessary features, like a headphone jack. The same trend applies to the calculator industry.

In their pursuit for minimalism, Cosio calculator company started to produce calculators that have a single display and can only compute trigonometric functions \t{sin}, \t{cos}, \t{tan} and their inverses \t{asin}, \t{acos}, \t{atan}.

Initially, the calculator's display shows the number $0$. After that, for each of the functions listed above, you can press a button that applies that function to the displayed number. If the operation is inapplicable or produces infinity, then the calculator breaks and stops responding.

You took it as a challenge to figure out what you can achieve using this calculator. Find a way to compute~$\frac {a}{b}$ using at most $1000$ operations.