AT_past19_l 最長のジグザグ

A length- $ k $ sequence $ A=(A_1,\ldots,A_k) $ is a zigzag sequence if: - $ A_1 < A_2> A_3 < A_4 > \ldots $ , or - $ A_1 > A_2 < A_3 > A_4

The input is given from Standard Input in the following format: > $ N $ $ B_1 $ $ \ldots $ $ B_N $

Print the answer in one line.

### Sample Explanation 1 The subsequence $ (5,2,4,3) $ of $ B $ is a zigzag sequence of length $ 4 $ . ### Constraints - $ 1\leq N \leq 2 \times 10^5 $ - $ 1\leq B_i\leq 10^9 $ - All input values are integers.