After beating his friends at their card game, Bob decides to make a few s'mores before retiring for the night. Bob loves s'mores, so he decides to build ~N~ campfires arranged neatly in a circle to roast his s'mores quickly. Unfortunately, he does not know how efficient each of the fires are, and it is here that he requires your help.

Each campfire ~x~ burns with a certain intensity ~I_x~. The variance of a campfire ~V_x~ is the larger of the absolute values of the difference in intensity between itself and either of the two adjacent fires, calculated as ~\max(|I_x - I_{x-1}|, |I_{x+1} - I_x|)~.

Little does he know that campfires must fulfill exactly one of two conditions to be able to cook s'mores as efficiently as possible.

• ~I_x \ge K~ — its intensity should be at least ~K~ degrees, otherwise the s'mores will not melt fast enough.
• ~V_x \le L~ — its variance should be at most ~L~ degrees, since similar fires will cook the s'mores evenly.

Input Specification

The input begins with three space-separated integers on one line ~N~ ~(3 \le N \le 500)~; ~K~, ~L~ ~(0 \le K, L \le 500)~, representing the number of campfires Bob absentmindedly built, the minimum recommended intensity, and the maximum recommended variance respectively.

The next ~N~ lines will each contain a single integer ~I_i~ ~(1 \le I_i \le 500)~, denoting the intensity of the ~i^{th}~ campfire, in the order in which Bob has arranged them.

Output Specification

Output a single integer, denoting the number of campfires Bob has built that can be used to cook s'mores efficiently.

Sample Input

3 2 1
1
2
1

Sample Output

2