states = ['1', '2' ,'3', '4']
final_states = ['3']

def run(string):
	next_state = '1'
	active_state = next_state
	for char in string:

		if active_state == '1':
			if char == 'a':
				next_state = '2'
			if char == 'b':
				next_stat_index = '4'

		if active_state == '2':
			if char == 'a':
				next_state = '4'
			if char == 'b':
				next_state = '3'

		if active_state == '3':
			if char == 'b':
				next_state = '3'
			if char == 'a':
				next_state = '3'
		if active_state == '4':
			if char == 'a':
				next_state = '3'
			if char == 'b':
				next_state = '2'


		active_state = next_state
		return active_state in final_states
if __name__ == '__main__':
		print(run('ab'))