Analyze the following state table. Which of the following descriptions is correct for the circuit to produce an output of $0?$

Hint: Convert to the state graph to facilitate analysis.

i$.$ Any input sequence ending with an odd number of $0\text{'}$s $,$ etc.$)$ followed by $10.$

ii$.$ Any input sequence ending with an odd number of $0\text{'}$s $,$ etc.$)$ followed by a single $1.$

iii. Any input sequence ending with an even number of $0\text{'}$s $,$ etc.$)$ followed by $10.$

iv$.$ Any input sequence ending with an even number of $0\text{'}$s $,$ etc.$)$ followed by a single $1.$

v$.$ Any input sequence ending with an even number of $0\text{'}$s $,$ etc.$)$ followed by $11.$