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: Accepted)

def main():
    from bisect import bisect_left
    from operator import itemgetter

    N, D, A = map(int, input().split())

    xh = []
    xs = set()
    for _ in range(N):
        x, h = map(int, input().split())
        xh.append((x, h))
        xs.add(x)
        xs.add(x + D)
        xs.add(x + D * 2)

    xh.sort(key=itemgetter(0), reverse=True)

    *xs, = sorted(xs)

    imos = [0] * (len(xs) + 10)
    mons = [0] * (len(xs) + 10)
    for x, h in xh:
        i = bisect_left(xs, x)
        mons[i] += h

    ret = 0
    for i in range(len(xs) + 1):
        d = (mons[i] - imos[i] + A - 1) // A
        if d > 0:
            ret += d
            imos[i] += d * A
            imos[bisect_left(xs, xs[i] + D * 2) + 1] -= d * A
        imos[i + 1] += imos[i]

    print(ret)


if __name__ == '__main__':
    main()

# import sys
#
# sys.setrecursionlimit(10 ** 7)
#
# input = sys.stdin.readline
# rstrip()
# int(input())
# map(int, input().split())