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: Time Limit Exceeded)

from bisect import bisect_right
from operator import itemgetter
import sys

def read():
    return sys.stdin.readline().rstrip()

def main():
    n, d, a = map(int, read().split())
    xh = [None] * n
    for i in range(n):
        xh[i] = tuple(map(int, read().split()))
    xh.sort(key=itemgetter(0))
    x, h = [0] * n, [0] * n
    for i, (xi, hi) in enumerate(xh):
        x[i] = xi
        h[i] = hi
    r = [0] * n
    for i, xi in enumerate(x):
        r[i] = bisect_right(x, xi + 2 * d) - 1
    cnt = 0
    for i, hi in enumerate(h):
        if hi <= 0:
            continue
        b = (hi + a - 1) // a
        cnt += b
        for j in range(i, r[i] + 1):
            h[j] -= a * b
    print(cnt)

if __name__ == "__main__":
    main()