Anton is under pressure --- he has to submit all the assignments. As often happens --- he cannot extend the deadline...
You are given a sequence of integers, and two integers and . You need to find the longest subsequence of the sequence such that (). Here, denotes the number of elements in the sequence . In other words, you need to select a subsequence such that the sum of any two adjacent numbers is not less than and not greater than .
A subsequence of an array is a sequence that can be obtained by deleting several (possibly none) elements from the original sequence.
输入格式
The first line contains three integers , , (, ).
The second line contains integers () --- the description of the sequence.
输出格式
Output a single integer --- the maximum length of such a subsequence .
样例
样例输入 1
5 2 6
1 3 4 2 5
样例输出 1
3
样例输入 2
2 1 1
1 1
样例输出 2
1
数据范围与提示
In the first example, you can select the subsequence . . .
