Problem Statement

Snuke bought a bridge of length L.
He decided to cover this bridge with blue tarps of length W each.
Below, a position on the bridge is represented by the distance from the left end of the bridge.
When a tarp is placed so that its left end is at the position $x (0 \leq x \leq L-W, x$ is real), it covers the range [x, x+W]. (Note that both ends are included.)
He has already placed N tarps.
The left end of the i-th tarp is at the position a_i.
At least how many more tarps are needed to cover the bridge entirely?
Here, the bridge is said to be covered entirely when, for any real number x between 0 and L (inclusive), there is a tarp that covers the position x.

Input

Input is given from Standard Input in the following format:
N L W
$a_1 \cdots a_N$

Output

Print the minimum number of tarps needed to cover the bridge entirely.

Constraints

• All values in input are integers.
• $1 \leq N \leq 10^{5}$
• $1 \leq W \leq L \leq 10^{18}$
• $0 \leq a_1 < a_2 < \cdots < a_N \leq L-W$

Sample Input 1

2 10 3
3 5

Sample Output 1

2

• The bridge will be covered entirely by, for example, placing two tarps so that their left ends are at the positions 0 and 7.

Sample Input 2

5 10 3
0 1 4 6 7

Sample Output 2

0

Sample Input 3

12 1000000000 5
18501490 45193578 51176297 126259763 132941437 180230259 401450156 585843095 614520250 622477699 657221699 896711402

Sample Output 3

199999992

见题面 Input 部分

见题面 Output 部分