A mountain range has 200 active volcanoes. In a particular year, 20% of the volcanoes exploded in the first two months, 40% of the remaining exploded by the half of the year, and at the end of the year, another 50% of the volcanoes that hadn't already erupted also exploded. How many mountains are still intact at the end of the year?
Please reason step by step, and put your final answer within \boxed{}.
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