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: Time Limit Exceeded)

import Control.Monad
import Data.List

main = do
  li <- getLine
  let [n,d,a] = map read $ words li
  xhs <- forM [1..n] (\_ -> do
    li <- getLine
    let [x,h] = map read $ words li
    return (x,h)
    )
  let ans = compute n d a xhs
  print ans

compute :: Int -> Int -> Int -> [(Int,Int)] -> Int
compute n d a xhs = loop 0 (sort xhs)
  where
    d2 = d * 2
    loop n [] = n
    loop n ((x,h):xhs) = loop (n+k) (xhs1a ++ xhs2)
      where
        k = (h + a - 1) `div` a
        ak = a * k
        xhs1 = takeWhile ((<= x + d2).fst) xhs
        xhs2 = drop (length xhs1) xhs
        xhs1a = [ (x1, h1 - ak) | (x1,h1) <- xhs1, h1 > ak ]