Fractions

For positive integers $a$ and $b$, we say that a fraction $\frac{a}{b}$ is *good* if it is equal to $\frac{m}{m+1}$ for some positive integer $m$. You are given an integer $N$. Find the number of pairs of integers $i, j$ such that $1 \le i, j \le N$ and the fraction $\frac{i}{i+1} \cdot \frac{j+1}{j}$ is good. ### Input The first and only line of the input contains a single integer $N$.