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 Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)
function bsearch(a,x);l,r=0,length(a)+1;while r-l>1;m=(r+l)>>1;if a[m]<=x;l=m;else;r=m;end;end;l;end
function bsearchg(a,x);l,r=0,length(a)+1;while r-l>1;m=(r+l)>>1;if a[m]<x;l=m;else;r=m;end;end;l;end
function main()
	n,d,a = readline() |> split |> parseMap
	b = Tuple{Int,Int}[(0,0) for i in 1:n]
	for i in 1:n
		p,q = readline() |> split |> parseMap
		b[i]=(p,q)
	end
	b = sort(b,by=x->x[1])
	x = [b[i][1] for i in 1:n]
	h = [b[i][2] for i in 1:n]
	lm = Int[0]
	v = Int[0]
	s = 0
	m = 1
	for i in 1:n
		r = bsearch(x,x[i]+2*d)
		l = bsearchg(lm,x[i]-2*d)
		if l==0
			y = cld(max(h[i]-v[m],0),a)
		else
			y = cld(max(h[i]-v[m]+v[l],0),a)
		end
		if y > 0
			push!(lm,x[i])
			s += y
			push!(v,v[m]+y)
			m += 1
		end
	end
	println(s)
end

main()