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 (7.3.0) (judge verdict: Wrong Answer)

import bisect
import itertools
import sys

input=sys.stdin.readline

def main(args):
    n, d, a = map(int,input().split())
    
    monster = [0]*n
    pos = [0]*n
    for i in range(n):
        x, h = map(int,input().split())
        monster[i] = (x, h)
        pos[i] = x
    
    pos.sort()
    monster.sort()
    
    #print(pos)
    
    limit = [0]*n
    #そのモンスターを攻撃したとき巻き添えにできるやつらの中で一番右のヤツのindex
    for i in range(n):
        limit[i] = bisect.bisect_right(pos, pos[i]+2*d)-1
    #print(limit)
    
    damage = [0]*n
    right = n-1
    left = 0
    for i in range(n):
        HP = monster[i][1]
        if i <= right:
            attack = -(-max(0, (HP-a*damage[left]))//a)
        if attack > 0:
            damage[i] += attack
            right = limit[i]
            left = i
        #print(damage)
            
    ans = list(itertools.accumulate(damage))
    print(ans[n-1])

if __name__ == '__main__':
    main(sys.argv[1:])