Say you want to traverse a list of integers starting at the first item and using each value as a pointer of what item to visit next. For example, you would traverse the list [1, 4, 3, 0, 2] in the following manner:

Because you visit every item once and go back to the starting point, the list [1, 4, 3, 0, 2] is a "full cycle".

Create a function that returns True if the input list is a full cycle, or False otherwise.

Examples

full_cycle([1, 4, 3, 0, 2]) ➞ True

full_cycle([1, 4, 0, 3, 2]) ➞ False

full_cycle([5, 3, 4, 2, 0, 1]) ➞ True

Notes

Test lists won't include any negative integers.