Around 1735, Swiss mathematician Leonard Euler fixed the famous Basel problem. He found an exact expression for the infinite sum \[ \sum_{i=1}^{\infty} \frac{1}{i^2} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \dots \]. Euler proved that this sum equals $$\frac{\pi^2}{6}$$. We write down the partial sums of this sequence as $$f_n$$. In other words, \[ f_n = \sum_{i=1}^n \frac{1}{i^2} \] For these partial sums, Euler proved that \[ \lim_{n\to\infty} f_n = \frac{\pi^2}{6} \]

Input

No input

Output

Two lines:

• first line: the value of $$f_{100}$$ as a decimal number,

• second line: the smallest value $$n \in \mathbb{N}$$ for which $$|f_n - \frac{\pi^2}{6}| \leq \frac{1}{100}$$.