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: Wrong Answer)

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

xh=[list(map(int, input().split())) for _ in range(n)]
xh.sort()

cnt=0

import heapq  # heapqライブラリのimport
#heapq.heapify(a)  # リストを優先度付きキューへ
#heapq.heappop(a)  # 最小値の取り出し
#heapq.heappush(a, -2)

bomb=0
he=[]
heapq.heapify(he)
dic={}

for i in range(n):
    (x,h)=xh[i]

    if bomb==0:
        secchi=x+d
        count=((-1*h)//a)*(-1)
        damage=count*a
        cnt+=count
        dic[secchi]=damage
        bomb+=damage
        heapq.heappush(he, secchi)
    else:
        while a:
            tmp=heapq.heappop(he)  
            if tmp+d<x:
                bomb-=dic[tmp]
            else:
                heapq.heappush(he, tmp)
                break
            if bomb==0:
                break

        if damage<h:
            h-=damage
            secchi=x+d
            count=((-1*h)//a)*(-1)
            damage=count*a
            cnt+=count
            dic[secchi]=damage
            bomb+=damage
            heapq.heappush(he, secchi)



print(cnt)