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>
        using namespace std;
        #define int long long
const int MAX = 1000001;
const int MOD = 1000000007;
   
        signed main() {
           int n,d,a;
           cin>>n>>d>>a;
           pair<int,int> p[n];
           int x,h;
           for(int i=0;i<n;i++){
               cin>>x>>h;
               p[i]=make_pair(x,(h-1)/a +1);
           }
           sort(p,p+n);
           int ans[n]={},k=0,j=0;
           for(int i=0;i<n;i++){
               while(p[j].first<p[i].first-2*d){
                   k-=ans[j];
                   j++;
               }
               ans[i]=max(0ll,p[i].second-k);
               k+=ans[i];
           }
           int ans2=0;for(int i=0;i<n;i++)ans2+=ans[i];
           cout<<ans2;


           return 0;

        }