문제<\/h2>
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.<\/p>
In their pursuit for minimalism, Cosio calculator company started to produce calculators that have a single display and can only compute trigonometric functions `sin<\/code>, cos<\/code>, tan<\/code> and their inverses asin<\/code>, acos<\/code>, atan<\/code>.<\/p>`
Initially, the calculator's display shows the number $0<\/mn><\/mrow>0<\/math><\/span><\/span> 0<\/span><\/span><\/span><\/span>. After that, for each of the functions listed above, you can press a button that applies that function to the displayed number. If the operation is inapplicable or produces infinity, then the calculator breaks and stops responding.<\/p> You took it as a challenge to figure out what you can achieve using this calculator. Find a way to compute a<\/mi>b<\/mi><\/mfrac><\/mrow>\frac {a}{b}<\/math><\/span><\/span> <\/span> <\/span> b<\/span><\/span><\/span><\/span> <\/span> <\/span><\/span> <\/span> a<\/span><\/span><\/span><\/span><\/span> <\/span><\/span> <\/span><\/span><\/span><\/span><\/span> <\/span><\/span><\/span><\/span><\/span> using at most 1000<\/mn><\/mrow>1000<\/math><\/span><\/span> 1000<\/span><\/span><\/span><\/span> operations.<\/p>$

Focusing on Costs