Alice and Bob are chocoholics and have invented their own chocolate game. At the start of each new game, they put $$n$$ chocolate bars in a row. Alice starts to eat the chocolate bars one by one from left to right, and Bob does the same from right to left. Alice and Bob eat the bars with equal speed, and for each chocolate bar it is known how long it takes to consume it (some bars take longer than others). When a player has consumed a chocolate bar, he or she immediately starts with the next in line. The rules of the game do not allow a player to eat two chocolate bars at the same time, to leave a bar unfinished and to make pauses. If both players can start eating the same bar simultaneously, Bob leaves it to Alice as a true gentleman.

How many chocolate bars will Alice and Bob have consumed at the end of a game?

Assignment

Write a function chocolate_bars that takes a list of strict positive integers as its argument. Each number in this list represents the time needed to eat the chocolate bar at the corresponding position. The function must return a tuple $$(a, b)$$, where $$a$$ is the number of chocolate bars consumed by Alice at the end of the game and $$b$$ the number of chocolate bars consumed by Bob.

Example

>>> chocolate_bars([2, 9, 8, 2, 7])
(2, 3)
>>> chocolate_bars([1, 2, 3, 4, 3, 2, 1])
(4, 3)