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 MAXN = 2e5+10;
long long f[MAXN];
long long n, d, a;

int main(){
    cin >>n>>d>>a;
    vector<pair<long long, long long>> m(n);

    for(int i=0;i<n;i++){
        long long x, h;
        cin >>x>>h;
        m[i] = make_pair(x, (h+a-1)/a);
    }

    sort(m.begin(), m.end());

    int l=0,r=0;
    long long cnt = 0;
    long long atk = 0;
    while(l<n){
        while(r<n && m[l].first + 2*d >= m[r].first)
            r++;

        atk += f[l];
        long long b = max(0LL, m[l].second - atk);
        cnt += b;
        atk += b;
        f[r] -= b;
        l++;
    }

    cout <<cnt;

}