Around 1735, Swiss mathematician Leonard Euler fixed the famous Basel problem1. 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 $\lim_{n\to\infty} f_n = \frac{\pi^2}{6}$

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 $$|f_n - \frac{\pi^2}{6}| \leq \frac{1}{100}$$.