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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
from bisect import bisect_left as bl
input = sys.stdin.readline
N, D, A = map(int, input().split())
a = []
b = []
res = 0
for _ in range(N):
  x, h = map(int, input().split())
  a.append([x, h])
  b.append(x)
a.sort(key = lambda x: x[0])
b.sort()
imos = [0] * (N + 2)
for i in range(N):
  a[i][1] += imos[i]
  imos[i + 1] += imos[i]
  if a[i][1] <= 0: continue
  l = a[i][0]
  r = a[i][0] + 2 * D
  t = bl(b, r)
  if t < N:
    if b[t] > r: t -= 1
  x = -(-a[i][1] // A)
  imos[i + 1] -= A * x
  imos[t + 1] += A * x
  a[i][1] = 0
  res += x
  #print(i, t)
  #print(a, imos)
#print(imos)
#print(a)
print(res)

"""
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ここでは他世界からの転生者は「旅行者 - tourist -」と呼ばれる。

不幸な交通事故から、社長 高橋直小はベラルーシに異世界転生してしまった。
"""