You've planted a new tree in your backyard. You're curious about how the diameter of the tree trunk changes over time. Obviously, the diameter never decreases—the tree only grows thicker over time—but during the spring the diameter increases most quickly, and during winter it barely increases at all.
From the data you've collected, you fit the following function for the diameter $$$d$$$ of the tree, given the time $$$t$$$ since you've planted it:
$$$d(t) = t + \sin t$$$.
Where the $$$\sin$$$ function takes in radians.
Now you want to know: given a target diameter $$$d_{\textrm{tar}}$$$, how long will it take for the tree to reach that diameter?
The only line of input contains a single real number $$$d_{\textrm{tar}}$$$: the target diameter of the trunk of your tree. This target diameter satisfies the bounds $$$0 \leq d_{\textrm{tar}} \leq 10^6.$$$
Print a single real number $$$t$$$: the time at which $$$d(t) = d_{\textrm{tar}}$$$.
To be judged correct, your answer must match the judge solution with relative or absolute error at most $$$10^{-4}$$$.
3.32
4.183233892618
1000000
1000000.178303
0
0
Hint: to make sure that your answer satisfies the above tolerance bound, be sure to print lots of digits (at least 5) after the decimal point!
