Design A Circuit That Can Detect 4 Consecutive 1'S. Draw State Diagram & State Table

Using the design procedure for sequential circuits, we have to design a circuit that can detect 4 consecutive 1s or more, there was a similar question but with 3 consecutive 1s or more, in that question, we had to make a state table and diagram with only 4 states (i.e: 00, 01, 10. 11), but in this question, I am confused that should i make 8 states (i.e: 000, 001, 010, 011, 100, 101, 110, 111) states or only 5 states (i.e.: 000, 001, 010, 011, 100: fifth state repeating itself when the input is 1 and return to base state when the input is 0).

My current guess is that I only need 5 states,

Present Input Next State Output

0 0 0 | 0 | 0 0 0 | 0

0 0 0 | 1 | 0 0 1 | 0

0 0 1 | 0 | 0 0 0 | 0

0 0 1 | 1 | 0 1 0 | 0

0 1 0 | 0 | 0 0 0 | 0

0 1 0 | 1 | 0 1 1 | 0

0 1 1 | 0 | 0 0 0 | 0

0 1 1 | 1 | 1 0 0 | 1

1 0 0 | 0 | 0 0 0 | 0

1 0 0 | 1 | 1 0 0 | 1

But I am confused while trying to find the equation of the 4 T flip flops using a k-map, should I include the same states with input 0 or should I just include the states with input 1 in the excitation table?