Score : $300$ points

Problem Statement

Every day, $N$ passengers arrive at Takahashi Airport. The $i$-th passenger arrives at time $T_i$.

Every passenger arrived at Takahashi airport travels to the city by bus. Each bus can accommodate up to $C$ passengers. Naturally, a passenger cannot take a bus that departs earlier than the airplane arrives at the airport. Also, a passenger will get angry if he/she is still unable to take a bus $K$ units of time after the arrival of the airplane. For that reason, it is necessary to arrange buses so that the $i$-th passenger can take a bus departing at time between $T_i$ and $T_i + K$ (inclusive).

When setting the departure times for buses under this condition, find the minimum required number of buses. Here, the departure time for each bus does not need to be an integer, and there may be multiple buses that depart at the same time.

Constraints

• $2 \leq N \leq 100000$
• $1 \leq C \leq 10^9$
• $1 \leq K \leq 10^9$
• $1 \leq T_i \leq 10^9$
• $C$, $K$ and $T_i$ are integers.

Input

The input is given from Standard Input in the following format:

$N$ $C$ $K$

$T_1$

$T_2$

$:$

$T_N$

Output

Print the minimum required number of buses.

5 3 5
1
2
3
6
12

3

For example, the following three buses are enough:

• A bus departing at time $4.5$, that carries the passengers arriving at time $2$ and $3$.
• A bus departing at time $6$, that carries the passengers arriving at time $1$ and $6$.
• A bus departing at time $12$, that carries the passenger arriving at time $12$.

6 3 3
7
6
2
8
10
6

3