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: Wrong Answer)

N,D,A = [int(i) for i in input().split()]
preXH = [[int(i) for i in input().split()] for j in range(N)]
preXH.sort()
XH = [[x,h//A + bool(h%A)] for x,h in preXH]

killed = 0
ans = 0
start = 0
nextstart = 0
while killed < N:
    x,h = XH[start]#左端の敵
    bonu = h#爆弾の回数
    hanni = x + 2*D
    XH[start][1] = 0
    killed += 1
    for m in range(start+1,N):
        x2,h2 = XH[m]
        if x2<=hanni and h2:
            XH[m][1] = max(0,h2-bonu)
            if h2<=bonu:killed+=1
            elif nextstart==start:#殺しきれなかった
                nextstart = m
        elif x2>hanni:break
    start = max(nextstart,start+1)
    ans += bonu
print(ans)