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 collections import defaultdict

n,d,a = map(int,input().split())

cnt = 0
arr = []
for i in range(n):
    x,h = map(int,input().split())
    arr.append([x,h])
arr.sort(key=lambda x:x[0])

# print("input finish")




class Bit:
    def __init__(self, n):
        self.size = n
        self.tree = defaultdict(int)

    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


bit = Bit(10**9+1)
edge = 10**9+1

# print("bit_prepared")

ans = 0
for i in range(n):
    x,h = arr[i]
    x += 1
    corr_left = max(1,x-d-1)
    corr_right = min(edge,x+d)
    # print(corr_left,corr_right)
    corr_cnt = bit.sum(corr_right)-bit.sum(corr_left)
    if corr_cnt*a >= h:
        continue
    else:
        rest = h-corr_cnt*a
        sup_cnt = (rest + (a - 1)) // a
        bit.add(corr_right,sup_cnt)
        ans += sup_cnt
    # print(ans)
print(ans)