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: Accepted)

#include<bits/stdc++.h>
#define int long long
#define rep(i, l, r) for(register int i = l; i <= r; ++ i)
using namespace std;
const int N = 200010;
inline int read()
{
	register char cc = getchar(); register int cn(0), flus(1);
	while(cc < '0' || cc > '9') {if(cc == '-') flus = - flus; cc = getchar();}
	while(cc >= '0' && cc <= '9') {cn = cn * 10 + cc - '0'; cc = getchar();}
	return cn * flus;
}
struct node
{
	int x,h;
} b[N];
inline bool cmp(node i,node j)
{
	return i.x < j.x;
}
int n, d, a, qn[N], qx[N], q1, q2, qs, ans;
signed main()
{
	n = read();
	d = read();
	a = read();
	rep(i, 1, n)
	{
		b[i].x = read();
		b[i].h = read();
		b[i].h=(b[i].h - 1) / a + 1;
	}
	sort(b+1,b+n+1,cmp);
	rep(i, 1, n)
	{
		while(qx[q1] < b[i].x && q1 < q2)
		{
			qs -= qn[q1++];
		}
		if(b[i].h > qs)
		{
			ans+=(qn[q2]=b[i].h-qs);
			qx[q2++]=b[i].x+ (d << 1);
			qs=b[i].h;
		}
	}
	printf("%lld\n",ans);
	return 0;
}