Inspired by Priyanshu Mishra

Consider any sequence of $2018$ positive integers $\{a_1, a_2, …, a_{2018}\}$ , and extend it periodically to an infinite sequence $\{a_1, a_2, …\}$ by defining $a_{i+2018} = a_i$ for all $i \geq 1$ . The sequence $\{a_1, a_2, …, a_{2018}\}$ is called Mishra-interesting if

• $1 \leq a_1 \leq a_2 \leq \cdots \leq a_{2018} \leq a_1 + 2018$ , and
• $a_{a_i} \leq i$ for $i=1,2,...,2018$ .

Let $N$ be the number of Mishra-interesting sequences $\{a_1, a_2, …, a_{2018}\}$ .

Submit the last $12$ digits of $N$ in base $10$ , i.e. submit $N \text{ mod } 10^{12}$ .

If there are an infinite number of Mishra-interesting sequences, submit $-1$ .

Inspired by this problem