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 Python (3.4.3) (judge verdict: Accepted)

def main():
    import sys
    from operator import itemgetter
    from collections import deque
    buf = sys.stdin.buffer
    
    n, d, a = map(int, buf.readline().split())
    m = map(int, buf.read().split())
    monsters = sorted(zip(m, m), key=itemgetter(0))
    
    bomb_area = deque([])
    bomb_power = deque([])
    total_damage = 0
    ans = 0
    for pos, hp in monsters:
        while bomb_area:
            area = bomb_area[0]
            if area < pos:
                bomb_area.popleft()
                power = bomb_power.popleft()
                total_damage -= power
            else:
                break
        if hp <= total_damage:
            continue
        else:
            count = (hp - total_damage + a - 1) // a
            ans += count
            power = a * count
            total_damage += power
            bomb_area.append(pos + 2 * d)
            bomb_power.append(power)
    print(ans)


if __name__ == '__main__':
    main()