CF930C Teodor is not a liar!

Young Teodor enjoys drawing. His favourite hobby is drawing segments with integer borders inside his huge $ [1;m] $ segment. One day Teodor noticed that picture he just drawn has one interesting feature: there doesn't exist an integer point, that belongs each of segments in the picture. Having discovered this fact, Teodor decided to share it with Sasha. Sasha knows that Teodor likes to show off so he never trusts him. Teodor wants to prove that he can be trusted sometimes, so he decided to convince Sasha that there is no such integer point in his picture, which belongs to each segment. However Teodor is lazy person and neither wills to tell Sasha all coordinates of segments' ends nor wills to tell him their amount, so he suggested Sasha to ask him series of questions 'Given the integer point $ x_{i} $ , how many segments in Fedya's picture contain that point?', promising to tell correct answers for this questions. Both boys are very busy studying and don't have much time, so they ask you to find out how many questions can Sasha ask Teodor, that having only answers on his questions, Sasha can't be sure that Teodor isn't lying to him. Note that Sasha doesn't know amount of segments in Teodor's picture. Sure, Sasha is smart person and never asks about same point twice.

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First example shows situation where Sasha can never be sure that Teodor isn't lying to him, because even if one knows $ cnt(x_{i}) $ for each point in segment $ [1;4] $ , he can't distinguish this case from situation Teodor has drawn whole $ [1;4] $ segment. In second example Sasha can ask about 5 points e.g. $ 1,2,3,5,6 $ , still not being sure if Teodor haven't lied to him. But once he knows information about all points in $ [1;6] $ segment, Sasha can be sure that Teodor haven't lied to him.