Shirt Color

Some students of the Federal University of Viçosa walk in the campus wearing a red shirt with the sentence: "This shirt is blue if you run fast enough". Tereu, one of the fastests students of the college, was shocked by the sentence written on the shirt and asked his teacher how the shirt could change its color. The professor said that an object can reflect the light in diffrent wavelengths and each wavelength is related to a color in the visible light, thus, let \(\lambda\) be this wavelength, the color will the determinated according with the following list:

• \(\lambda\) \(<\) \(400 nm\): invisivel (invisible)
• \(400 nm\) \(\leq\) \(\lambda \) \(<\) \(425 nm\): violeta (violet)
• \(425 nm\) \(\leq\) \(\lambda \) \(<\) \(445 nm\): anil (indigo)
• \(445 nm\) \(\leq\) \(\lambda \) \(<\) \(500 nm\): azul (blue)
• \(500 nm\) \(\leq\) \(\lambda \) \(<\) \(575 nm\): verde (green)
• \(575 nm\) \(\leq\) \(\lambda \) \(<\) \(585 nm\): amarelo (yellow)
• \(585 nm\) \(\leq\) \(\lambda \) \(<\) \(620 nm\): laranja (orange)
• \(620 nm\) \(\leq\) \(\lambda \) \(<\) \(750 nm\): vermelho (red)
• \(\lambda \geq\) \(750 nm\): invisivel (invisible)

The words between the parentheses are the translates of the colors in portuguese, but it cannot be printed on the output, which has to present the words in portuguese.

The change of the color happens because when an observer moves, it sees a wavelength \(\lambda'\), which is diffrent from the \(\lambda\) real one. This phenomenon is called "Doppler Effect" and it's matematically explained by the formula (it works when we consider positive the velocity when the observer approaches the source):

\({\lambda' - \lambda\over\lambda} = \sqrt{c - v\over{c + v}} -1 \)

\(v\) is the speed of the observer and \(c\) is the speed of light in the vacuum.

The shirt is red and it reflects the light in the wavelength \(\lambda = 700 nm\), the speed of light in the vacuum is \(c = 3\times10^8 m/s\).

Tereu would see the shirt in a wavelenght \(\lambda' = 495 nm\), that is, blue, if he reached a speed close of \(10^8 m/s\). He knows he is not able to reach this velocity, then, he wants you to create a program which returns the color he would see if he was in a speed V.