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 (3.8.2) (judge verdict: Accepted)

from math import ceil
N,D,A = list(map(int, input().split()))
P = []
for _ in range(N):
  P.append(list(map(int, input().split())))
  # X,H

P.sort()

#for p in P:
#  print(p)
  
# Attack[i] : i番目（Xi）を左端に爆弾を投げたとき、巻き込める最大の番号Xj
Attack = [-1 for _ in range(N)]
leftx, leftj = 0,0
for i in range(N):
  now = P[i][0]
  leftx = now + 2*D
  while leftj < N:
    if P[leftj][0] <= leftx:
      leftj += 1
    else:
      break
  Attack[i] = leftj - 1
  
#print(Attack)
# damage管理
# 範囲攻撃はimosっぽくやる。届いた左端に+Dして、届いた右端の右隣に-Dする
# 今までのダメージ総和をworkとして持ちつつ、imosで回復すればよい
wk_dam = 0
imos = [0] * (N+1)
ans = 0
for i in range(N):
  wk_dam += imos[i]
  #print(i,wk_dam,P[i][1],ans)
  if P[i][1] <= wk_dam:
    # すでに累積ダメージで死んでる
    continue
  cnt = (P[i][1] - wk_dam + A-1) // A # ceil(zanHP / A)
  wk_dam += cnt * A
  imos[i] += cnt * A
  imos[Attack[i]+1] -= cnt * A
  ans += cnt
  
print(ans)
#print(imos)