State a loop invariant that is strong enough to prove the below algorithm is correct and PROVE it according to loop correctness rules

• Initialization: It is true before the loop runs.
• Maintenance: If it's true before an iteration of a loop, it remains true before the next iteration.
  • Termination: It will terminate in a useful way once it is finished.

    some values

    X	n	F(x,n)
    1	1	1
    2	2	1
    3	2	1
    4	3	2
    5	3	2
    8	4	2
    10	4	3
    15	4	3
    16	5	4
    1522756	21	1234

Consider the following algorithm. 1 F(x, n) % precondition: n is a positive integer and r is a positive n-bit integer (i.e., 2"-1