P9825 [ICPC 2020 Shanghai R] Fibonacci

In mathematics, the Fibonacci numbers, commonly denoted as $f_n$, is a sequence such that each number is the sum of the two preceding numbers, starting with $1$ and $1$. That is, $f_1 = 1, f_2 = 1$ and $f_n = f_{n-2} + f_{n-1}~(n \ge 3)$. Thus, the beginning of the sequence is $1, 1, 2, 3, 5, 8, 13, 21,\ldots$ . Given $n$, please calculate $\sum_{i=1}^{n}{\sum_{j=i+1}^{n}{g(f_i,f_j)}}$, where $g(x,y) = 1$ when $x \cdot y$ is even, otherwise $g(x,y) = 0$.

The only line contains one integer $n~(1\le n\le 10^9)$.

Output one number -- $\sum_{i=1}^{n}{\sum_{j=i+1}^{n}{g(f_i,f_j)}}$.