Which would be the best type of engine for F1 cars.2 stroke or 4 stroke?

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It is quite evident from past that 2 stroke engines have dominated over the power issue in comparison to 4 stroke engines. Ihave seen many arguements on whether a four stroke is powerful or 2 stroke. Well 3 stroke has pollution problem as major and very few other minor problems or obstacles. But certainly when i have worked out the economics i found 2 strokes were on the leader board. The F1 racing has now made it mandatory that there should be only 4 stroke engines used. Well i am very much sure that this change was because of pollution and not power. There are many un scientific people who make an opinion that 4 stroke engines are powerful than 2 stroke. Well check this out those guys who say this..For a 250 cc 2 stroke a four stroke engines with almost 500cc needs to be compared as 2 stroke produces power on every stroke rather than a 4 stroke. Well the usage of cc clearly describes 4 stroke can never be compared on same ground with 2 stroke for power output..! Well only plus point of 4 stroke is the noise from eshaust. But i suggest that is because of well researched and developed exhaust system. Not much research has been made upon 2 strokes exhaust system. And i have good news that an EFI 2 stroke engine is emitting very less smoke as compared to traditional 2 stroke. And there is one more wrong beleif that 4 strokes do not pollute. it doesnt emit smoke but that doesnt mean that it doesnt emit pollution. it does.Well efi 2 and 4 stroke are almost similar on grounds in terms of pollutant emmisions.! hard to beleive but its true..!! I wuld personally and technically feel that f1 should have 2 stroke engines rather than 4 strokes for real speed entertainment..!! what do you think?? Also i need info whether there are any f1 2 stroke engines or not