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: Wrong Answer)

#include <algorithm>
#include <array>
#include <cmath>
#include <cstdio>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <vector>
using namespace std;
using ll=long long int;
using vi=vector<int>;
using vl=vector<ll>;
using vs=vector<string>;
constexpr int INF=1<<30;
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define FORR(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define RANGE(i,a,b) for(int i=(a);i<=(b);i++)
#define RANGER(i,a,b) for(int i=(b);i>=(a);i--)
#define REP(i,n) FOR(i,0,n)
#define REPR(i,n) FORR(i,0,n)

#define EVAL 1

#ifdef EVAL
#define LOG(i) 0
#else
#define LOG(i) cerr<<#i<<": "<<i<<endl
#endif

struct monst{ // also, attack.
	int pos,hp;
};
auto M=vector<monst>(2e5);
void solve(){
	int N,D,A,ans=0;
	cin>>N>>D>>A;
	int X,H;
	REP(i,N){
		scanf("%d%d",&X,&H);
		M[i]={X,H};
	}
	sort(&M[0],&M[N],[](auto a,auto b){return a.pos<b.pos;});
	//REP(i,N)LOG(M[i].pos);
	queue<monst> atks;
	int atk=0;
	REP(i,N){
		auto m=M[i];
		while(atks.size()>0&&atks.front().pos+N<m.pos){
			atk-=atks.front().hp;
			atks.pop();
		}
		if(m.hp>atk){
			int neededbombs=(m.hp-atk+A-1)/A;
			int bombhp=neededbombs*A;
			atk+=bombhp;
			atks.push({m.pos+N,bombhp});
			LOG(m.pos+N);
			LOG(bombhp);
			ans+=neededbombs;
		}
	}
	cout<<ans<<endl;
	//cout<<(H<=0?"Yes":"No")<<endl;
}
int main(){
	solve();
	return 0;
}