Beautiful Subsequence

You are given an array $A$ of size $2N$, where every number from $1$ to $N$ occurs **exactly twice**. Consider choosing a subsequence of positions $t = (t_1, t_2, \ldots, t_M)$ with $1 \le t_1 < t_2 < \cdots < t_M \le 2N$. This subsequence is called **valid** if for every starting point $j$ with $1 \le j \le M - N + 1$, the values $A_{t_j}, A_{t_{j+1}}, \ldots, A_{t_{j+N-1}}$ are all **mutuall