Problem:
Score : 600 points

Problem Statement

Silver Fox is fighting with N monsters.

The monsters are standing in a row, and we can assume them to be standing on a number line. The i-th monster, standing at the coordinate X_i, has the health of H_i.

Silver Fox can use bombs to attack the monsters.
Using a bomb at the coordinate x decreases the healths of all monsters between the coordinates x-D and x+D (inclusive) by A.
There is no way other than bombs to decrease the monster's health.

Silver Fox wins when all the monsters' healths become 0 or below.

Find the minimum number of bombs needed to win.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq D \leq 10^9

1 \leq A \leq 10^9

0 \leq X_i \leq 10^9

1 \leq H_i \leq 10^9

X_i are distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N D A
X_1 H_1
:
X_N H_N

Output

Print the minimum number of bombs needed to win.

Sample Input 1

3 3 2
1 2
5 4
9 2

Sample Output 1

2

First, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.

Then, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.

Now, all the monsters' healths are 0.
We cannot make all the monsters' health drop to 0 or below with just one bomb.

Sample Input 2

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5

Sample Output 2

5

We should use five bombs at the coordinate 5.

Sample Input 3

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Sample Output 3

3000000000

Watch out for overflow.

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

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import Data.List (mapAccumL, sort)

main :: IO ()
main = do
  (n : d : a : _) <- map unsafeTextToInt . T.words <$> T.getLine :: IO [Int]
  let
    walk :: [(Int, Int)] -> [(Int, Int)] -> [(Int, Int)]
    walk = fmap (snd .) $ flip $ mapAccumL step . (,) (0, 0)
      where
        step ((l, c), yks) (x, h) = (((succ (l - l'), c - c' + k'), yks'), (x, k'))
          where
            v = take l yks
            u = takeWhile ((< x - 2 * d) . fst) v
            (l', c') = lenSum u
            k' = (max 0 (h - (c - c') * a) + a - 1) `div` a
            yks' = drop l' yks
    
    lenSum :: [(Int, Int)] -> (Int, Int)
    lenSum = foldl step (0, 0)
      where
        step (l, s) (_, h) = (succ l, s + h)

    
  xhs <- sequence . replicate n $ unsafeListToTuple . map unsafeTextToInt . T.words <$> T.getLine :: IO [(Int, Int)]
  print . sum . map snd . fix . walk . sort $ xhs

fix :: (a -> a) -> a
fix f = x
  where
    x = f x

unsafeListToTuple :: [Int] -> (Int, Int)
unsafeListToTuple (x : y : _) = (x, y)

unsafeTextToInt :: T.Text -> Int
unsafeTextToInt s = case T.signed T.decimal s of
  Right (n, _) -> n