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)

import bisect

n, d, a = map(int, input().split())
xh = []
for i in range(n):
    xh.append(list(map(int, input().split())))
xh.sort()
x = [xh[i][0] for i in range(n)]
h = [xh[i][1] for i in range(n)]
count = 0
min_x = 0
acm = [0] * (n + 1)
dif = [0] * (n + 1)
while min_x < n:
    place = x[min_x] + d
    num = (h[min_x] - acm[min_x + 1] - 1) // a + 1
    count += num
    dif[min_x] += num
    dif[bisect.bisect(x, place + d)] -= num
    for i in range(min_x, bisect.bisect(x, place + d)):
        acm[i + 1] = acm[i] + dif[i] * a
        if acm[i + 1] >= h[i]:
            min_x += 1
            continue
        else:
            break
print(count)