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)

N,D,A=map(int,input().split())
monster=[]
for i in range(0,N):
    x,h=map(int,input().split())
    monster.append([x,h])

monster.sort()

H=[monster[i][1] for i in range(0,N)]

right_2d=[0 for i in range(0,N)]
for i in range(0,N):
    start=i
    end=N-1
    while end-start>1:
        test=(end+start)//2
        if 2*D+monster[i][0]>=monster[test][0]:
            start=test
        else:
            end=test
    if 2*D+monster[i][0]>=monster[end][0]:
        right_2d[i]=end
    else:
        right_2d[i]=start

imos=[0 for i in range(0,N+1)]
ans=0
for i in range(0,N):
    H[i]-=imos[i]
    if H[i]>0:
        count=(H[i]+A-1)//A
        ans+=count
        imos[i]+=A*count
        imos[right_2d[i]+1]-=A*count

    imos[i+1]+=imos[i]

print(ans)