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 C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;
const int N=2e5+10;
struct node
{
	int pos,h;
}a[N];
bool cmp(node x,node y)
{
	return x.pos<y.pos;
}
int main()
{
    ios::sync_with_stdio(0);
    int n,d,attack; cin>>n>>d>>attack;
    for(int i=0;i<n;i++)
		 cin>>a[i].pos>>a[i].h;
	sort(a,a+n,cmp);

	int cur=a[0].pos; LL ans=0;
	for(int i=0;i<n;)
	{
		 int cou=a[i].h/attack+(int)(a[i].h%attack!=0);
		int j,flag=0,cc;
		 for(j=i;j<n&&a[j].pos<=cur+2*d;j++)
		 {
			a[j].h-=cou*attack;
			if(!flag&&a[j].h>0)
			{
				cc=a[j].pos;
				i=j,flag=1;
			}
		 }
		 if(!flag) i=j,cc=a[j].pos;
		 cur=cc;
      ans+=cou;
	}
	cout<<ans<<endl;

    return 0;
}