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)

import bisect
import sys
input = sys.stdin.readline
from collections import defaultdict
class Bit:
  def __init__(self, n):
    self.size = n
    self.tree = [0] * (n + 1)

  def sum(self, i):
    s = 0
    while i > 0:
        s += self.tree[i]
        i -= i & -i
    return s

  def add(self, i, x):
    while i <= self.size:
      self.tree[i] += x
      i += i & -i
n,d,a = map(int,input().split())
xh = [list(map(int,input().split())) for i in range(n)]
for i in range(n):
  xh[i][1] = (xh[i][1]+a-1)//a
xh.sort()
x = [xh[i][0] for i in range(n)]
remain = [xh[i][1] for i in range(n)]
ans = 0
bit = Bit(n)
for i in range(n):
  if bit.sum(i+1) >= remain[i]:
    continue
  br = bisect.bisect_right(x,x[i]+2*d)
  ans += remain[i]
  bit.add(i+1,remain[i])
  bit.add(br+1,-remain[i])
print(ans)