AT_agc078_b [AGC078B] L Robust IS

You are given a length- $ N $ sequence of positive integers $ A=(A_1,A_2,\ldots,A_N) $ and non-negative integers $ X,Y $ . Find the maximum length $ M $ of a subsequence $ B=(B_1,B_2,\ldots,B_M) $ of $ A $ that satisfies both of the following conditions. - $ B_i\ge B_{i-1}-X $ holds for every integer $ i $ satisfying $ 2\le i\le M $ . - $ B_i\ge B_{i-2}-(X+Y) $ holds for every integer $ i $ satisfying $ 3\le i\le M $ .

The input is given from Standard Input in the following format: > $ N $ $ X $ $ Y $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Output the answer.

### Sample Explanation 1 The subsequence $ (8,6,7,5,6) $ satisfies the conditions. There is no subsequence of length $ 6 $ or greater that satisfies the conditions, so output $ 5 $ . ### Constraints - $ 1\le N\le 5\times 10^5 $ - $ 1\le A_i\le 10^9 $ - $ 0\le X,Y\le 10^9 $ - All input values are integers.