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