Problem:
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.

Sample Input 1

5 3 5
1
2
3
6
12

Sample Output 1

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.

Sample Input 2

6 3 3
7
6
2
8
10
6

Sample Output 2

3

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE BangPatterns #-}
import           Control.Exception           (assert)
import           Control.Monad
import           Control.Monad.Primitive
import qualified Control.Monad.ST            as ST
import qualified Data.Array.IO               as IO
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as A
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Foldable
import           Data.List
import qualified Data.Map.Strict             as Map
import           Data.Maybe
import qualified Data.Sequence               as Seq
import qualified Data.Set                    as Set
import qualified Data.Vector                 as VB
import qualified Data.Vector.Mutable         as VBM
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM
import           Debug.Trace

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
getIntVec n = V.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

readInteger = fst . fromJust . BS.readInteger
readIntegerList = map readInteger . BS.words
getInteger = readInteger <$> BS.getLine
getIntegerList = readIntegerList <$> BS.getLine

inf :: Int
inf = 10^18

quickSortList :: (Ord a, VM.Unbox a) => [a] -> [a]
quickSortList xs = ST.runST $ do
    arr <- V.thaw $ V.fromList xs
    let beg = 0
        end = VM.length arr - 1
    quickSortVec beg end arr
    V.toList <$> V.freeze arr

quickSortVec l u arr
  | l >= u    = return ()
  | otherwise = do
      VM.unsafeSwap arr l ((u+l)`div`2)
      t <- VM.unsafeRead arr l
      let i = l
          j = u + 1
      nj <- loopVec t u i j arr
      VM.unsafeSwap arr l nj
      quickSortVec l (nj-1) arr
      quickSortVec (nj+1) u arr

loopVec !t !u !i !j arr = do
  ni <- doWhile i (+1)         (< t)
  nj <- doWhile j (subtract 1) (> t)
  if ni > nj
    then return nj
    else do VM.unsafeSwap arr ni nj
            loopVec t u ni nj arr
              where
                {-# INLINE doWhile #-}
                doWhile k op p
                  | nk > u    = return nk
                  | otherwise = do
                      x <- VM.unsafeRead arr nk
                      if p x then
                        doWhile nk op p
                        else
                        return nk
                        where
                          nk = op k

main = do
  [n, c, k] <- getIntList

  ts0 <- replicateM n getInt
  let ts = quickSortList ts0

  let solve ts@(x:xs) t res = let t' = x + k
                                  ts' = dropNWhile c t' ts
                              in solve ts' t' (res+1)
      solve [] _ res = res

      dropNWhile _ _ [] = []
      dropNWhile n t xs@(x:xs') | n == 0 || x > t = xs
                                | otherwise = dropNWhile (n-1) t xs'

  print $ solve ts 0 0