El Hurón Legendario was given a magical circular array $$$A=[a_1,a_2,\dots,a_n]$$$ of size $$$n$$$ as a Christmas present last December. Since the array is circular, $$$a_1$$$ and $$$a_n$$$ are adjacent.

For a pair of positive integers $$$x$$$ and $$$y$$$, we say that $$$y$$$ is $$$A$$$-reachable from $$$x$$$ if $$$x$$$ can be transformed into $$$y$$$ by using the following four-step operation any number of times:

1. Choose an element $$$a_i$$$ of $$$A$$$, such that $$$\gcd(x,a_i) \gt 1$$$.
2. Choose a prime divisor $$$d$$$ of $$$\gcd(x,a_i)$$$.
3. Choose a divisor $$$e$$$ of $$$a_i$$$, such that $$$e$$$ is prime or equal to $$$1$$$.
4. Set $$$x := x \cdot \frac{e}{d}$$$.

After playing with his magical array during a month and using it to transform all the integers less or equal to $$$2025!^{2025!}$$$, El Hurón Legendario wants to save space in its array box. For that reason, he wants to cut some subarray of his circular array and throw away the rest of it. He wants the chosen subarray to be equivalent to the original array. A subarray $$$A'$$$ of $$$A$$$ is equivalent to $$$A$$$, if, for all $$$x,y \in \mathbb{Z}^+$$$, $$$y$$$ is $$$A'$$$-reachable from $$$x$$$ if and only if it is $$$A$$$-reachable from $$$x$$$.

Help El Hurón Legendario find the smallest equivalent subarray he can cut.