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 collections import deque
import sys

input = sys.stdin.buffer.readline
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))

n, d, a = MAP()
xh = [LIST() for i in range(n)]

xh = sorted(xh, key=lambda x:(x[0]))
q = deque()
ca = 0
cnt = 0
for i in range(n):
    cx, ch = xh[i][0], xh[i][1]
    
    while q and q[0][0] < cx:
        qx, qa = q.popleft()
        ca -= qa
    
    if ch - ca <= 0:
        continue
    
    cn = (ch - ca + a - 1) // a
    cnt += cn
    ca += cn * a
    q.append([cx+2*d, cn*a])
    
print(cnt)