Problem: 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.

Examples

Input

3 3 2
1 2
5 4
9 2


Output

2


Input

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5


Output

5


Input

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000


Output

3000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;
const int N=2e5+5,INF=2e9;
#define ll long long
pair<ll,ll> a[N];
ll cum[N];
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
    int n,D,A;
    cin>>n>>D>>A;
    for(int i=0;i<n;i++)
        cin>>a[i].first>>a[i].second;
    sort(a,a+n);
    ll cur=0,ans=0;
    for(int i=0;i<n;i++)
    {
        cur+=cum[i];
        ll H=a[i].second-cur;
        ll need=max(0ll,(H+A-1)/A);
        cur+=need*A;
        ans+=need;
        pair<ll,ll> p={a[i].first+2*D,(ll)INF};
        int idx=upper_bound(a,a+n,p)-a;
        cum[idx]-=need*A;
    }
    cout<<ans<<endl;
    return 0;
}