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: Time Limit Exceeded)

from operator import itemgetter
from math import ceil
def main():
	a=[]
	c = [int(i) for i in input().split()]
	N=c[0]
	D=c[1]
	A=c[2]
	count=0
	for i in range(N):
		c = [int(i) for i in input().split()]
		a.append(c)
	a = sorted(a, key=itemgetter(0))
	if (a[-1][0]-a[0][0] <= 2*D):
		max = a[0][1]
		for i in range(1,N):
			if (max<a[i][1]):
				max = a[i][1]
		count = ceil(max/A)
		print (count)
		return
	elif (D==0):
		sum =0
		for i in range(N):
			count+=ceil(a[i][1]/A)
		print (count)
		return
	k=0
	while (1):
		d = ceil(a[k][1]/A)
		count+=d
		kold = k
		a[k][1]=0
		found =0
		for i in range(kold+1,N):
			if (a[i][1]<=0):
				continue
			if(a[i][0]<=(a[kold][0]+2*D)):
				a[i][1]-=(d*A)
				if (found==0 and a[i][1]>0):
					k=i
					found =1
			else:
				if (found==0):
					k=i
					found=1
				break
		if (found==0):
			break
	print (count)
if __name__== "__main__":
	main()