There is a sequence of integers. Your task is to find the longest subsequence that satisfies the following condition: the difference between the maximum element and the minimum element of the subsequence is no smaller than m and no larger than k.

There are multiple test cases. For each test case, the first line has three integers, n, m and k. n is the length of the sequence and is in the range [1, 100000]. m and k are in the range [0, 1000000]. The second line has n integers, which are all in the range [0, 1000000]. Proceed to the end of file.

For each test case, print the length of the subsequence on a single line.

2010 ACM-ICPC Multi-University Training Contest（10）——Host by HEU