Floyd's Tortoise and Hare Meeting Point

A singly linked list has 8 nodes, labelled $0, 1, \dots, 7$ in order from the head. Node $i$ points to node $i+1$ for $i = 0, \dots, 6$, and the tail node $7$ points back to node $3$, creating a cycle.

To detect the cycle, Floyd's algorithm starts two pointers, slow and fast, both at node $0$. In each iteration slow advances one node and fast advances two nodes. The algorithm stops at the first iteration after which both pointers are on the same node.

How many iterations are performed, counting the iteration in which they first meet?