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: Wrong Answer)

n,d,a=map(int,input().split())
xh=[list(map(int,input().split())) for _ in range(n)]
xh.sort()

ans = 0
totalDamage = 0
import queue
q=queue.Queue()
firstTime =True
for i in range(n):
    x,h = xh[i]
    if totalDamage == 0:
        ans += (h+a-1)//a
        damege = (h+a-1)//a*a
        totalDamage += damege
        q.put((x+2*d, damege))
    else:
        if firstTime:
            preX, preDamege = q.get()
            firstTime =False
            
        while(preX < x):
            totalDamage -= preDamege
            if q.empty():
                firstTime = True
                break
            preX, preDamege = q.get()
        
        h -= totalDamage
        ans += (h+a-1)//a
        damege = (h+a-1)//a*a
        totalDamage += damege
        q.put((x+2*d, damege))
print(ans)