Biquadratic Equation

Input

You will receive a single line containing three numbers separated by spaces, representing the coefficients of the biquadratic equation: $a$, $b$, and $c$. The absolute values of these coefficients do not exceed $100$.

Output

Output a single line in one of the following formats:

• If there are no roots, print "No roots" (without quotes).

• If there is one root, print "One root:" (without quotes) followed by the root (separated by a space).

• If there are two roots, print "Two roots:" (without quotes) followed by the smaller root and then the larger root (separated by spaces).

• If there are three roots, print "Three roots:" (without quotes) followed by the three roots in ascending order (separated by spaces).

• If there are four roots, print "Four roots:" (without quotes) followed by the roots in ascending order (separated by spaces).

• If there are infinitely many roots, print "Many roots" (without quotes).

All roots must be printed with a precision of 10^{-3}.

Examples