CF545C Woodcutters

Little Susie listens to fairy tales before bed every day. Today's fairy tale was about wood cutters and the little girl immediately started imagining the choppers cutting wood. She imagined the situation that is described below. There are $ n $ trees located along the road at points with coordinates $ x_{1},x_{2},...,x_{n} $ . Each tree has its height $ h_{i} $ . Woodcutters can cut down a tree and fell it to the left or to the right. After that it occupies one of the segments $ [x_{i}-h_{i},x_{i}] $ or $ [x_{i};x_{i}+h_{i}] $ . The tree that is not cut down occupies a single point with coordinate $ x_{i} $ . Woodcutters can fell a tree if the segment to be occupied by the fallen tree doesn't contain any occupied point. The woodcutters want to process as many trees as possible, so Susie wonders, what is the maximum number of trees to fell.

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In the first sample you can fell the trees like that: - fell the $ 1 $ -st tree to the left — now it occupies segment $ [-1;1] $ - fell the $ 2 $ -nd tree to the right — now it occupies segment $ [2;3] $ - leave the $ 3 $ -rd tree — it occupies point $ 5 $ - leave the $ 4 $ -th tree — it occupies point $ 10 $ - fell the $ 5 $ -th tree to the right — now it occupies segment $ [19;20] $ In the second sample you can also fell $ 4 $ -th tree to the right, after that it will occupy segment $ [10;19] $ .