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 Python (3.4.3) (judge verdict: Wrong Answer)

from bisect import bisect_left
import math
import sys
from collections import deque
readlines = sys.stdin.readline

def main():
  n,d,a = map(int,input().split())
  xx = []
  hh = []
  X = []
  H = []
  for _ in range(n):
    tmp = list(map(int,input().split()))
    xx.append(tmp[0])
    hh.append(tmp[1])

  k = zip(xx,hh)
  q = sorted(k)
  for xxx,hhh in q:
    X.append(xxx)
    H.append(hhh)
  X = deque(X)
  H = deque(H)
  ans = 0
  end = n-1
  while True:
    x = X[end] - d
    start = bisect_left(X,x-d)
    num = math.ceil(H[end] / a)
    ans += num
    H.pop()
    X.pop()
    e = end
    end = start-1
    A = a * num
    for i in range(start,e):
      h = H.pop()
      if h > A:
        H.append(h-A)
      else:
        X.pop()

    if end < 0:
      break

  print(ans)
if __name__ == '__main__':
  main()