CF939F Cutlet

Arkady wants to have a dinner. He has just returned from a shop where he has bought a semifinished cutlet. He only needs to fry it. The cutlet should be fried for $ 2n $ seconds, in particular, it should be fried for $ n $ seconds on one side and $ n $ seconds on the other side. Arkady has already got a frying pan and turn on fire, but understood that maybe he won't be able to flip the cutlet exactly after $ n $ seconds after the beginning of cooking. Arkady is too busy with sorting sticker packs in his favorite messenger and can flip the cutlet only in some periods of time. Namely, there are $ k $ periods of time in which he can do it, the $ i $ -th of them is an interval of time from $ l_{i} $ seconds after he starts cooking till $ r_{i} $ seconds, inclusive. Arkady decided that it's not required to flip the cutlet exactly in the middle of cooking, instead, he will flip it several times in such a way that the cutlet will be fried exactly $ n $ seconds on one side and $ n $ seconds on the other side in total. Help Arkady and find out if it's possible for him to cook the cutlet, if he is able to flip the cutlet only in given periods of time; and if yes, find the minimum number of flips he needs to cook the cutlet.

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In the first example Arkady should flip the cutlet in time moment $ 3 $ seconds after he starts cooking and in time moment $ 13 $ seconds after he starts cooking. In the second example, Arkady can flip the cutlet at $ 10 $ seconds after he starts cooking.