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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
  "fmt"
  "sort"
)

type DArray [][]int
func (a DArray) Len() int { return len(a) }
func (a DArray) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
func (a DArray) Less(i, j int) bool { return a[i][0] < a[j][0] }

func main() {
  var N, D, A int
  fmt.Scan(&N, &D, &A)
  M := make(DArray, N)
  for i := 0; i < N; i++ {
    var x, h, z int
    fmt.Scan(&x, &h)
    if h % A >= 1 {
      z = 1
    } else {
      z = 0
    }
    M[i] = []int{x, h / A + z}
  }
  sort.Sort(M)

  rng := 2 * D + 1
  atk := 0
  for i := 0; i < N; i++ {
    if M[i][1] > 0 {
      atk += M[i][1]
    } else {
      continue
    }
    for j:= i+1; j < N; j++ {
      if M[j][0] - M[i][0] > rng {
        break
      }
      M[j][1] -= M[i][1]
    }
  }
  fmt.Println(atk)
}