Like any other teenager, teen cows are occasionally overtaken by fads. Sometimes it's a hula hoop or a pet rock, other times it's Counterstrike, Pokemon, Rick Astley, or tribal tattoos on their udders.

Mathematically, we know that a fad has an initial attractiveness level $L$ ($1 \le L \le 50,000$). Cow $i$ has a resistance ($0 \le R_{i} \le 1,000,000$) that tells how long she can avoid a fad before having no alternative but to participate. When a fad's attractiveness level meets or exceeds a cow's fad resistance, then the cow will want to participate in the fad.

Each cow who participates in a fad increases (through peer pressure) that fad's attractiveness by some value $K$ ($1 \le K \le 2,500$).

Given a population of $N$ ($1 \le N \le 100,000$) cows, determine how many will participate in a fad.

Input

• Line 1: Three space-separated integers: $N$, $L$, and $K$
• Lines $2..N+1$: Line $i+1$ contains cow $i$'s a single integer that is fad resistance: $R_{i}$

Output

• Line 1: A single integer that is the number of cows how ultimately participate in the fad.

Examples

Input 1

5 2 3
2
6
12
5
14

Output 1

3

Five cows with fad resistances 2, 6, 12, 5, and 14. Initial fad attractiveness is 2; peer pressure adds 3 for each attractiveness index for each cow that participates.

The initial attraction level of 2 brings in cow #1 (whose resistance is 2) and raises the attractiveness level to 5, thus attracting cow #4 (whose resistance is 5) and raising the attractiveness level to 8. This attracts cow #2 (resistance: 6) and raises the attractiveness level to 11. Neither cow #3 (resistance: 12) or cow #5 (resistance: 14) is sucked into the fad; a total of 3 cows particpate.

Problem credits: Jarrah Lacko, 2009