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;using L = long long;using V= pair<L,L>;
#define F first
#define S second
#define I XH[i]
#define R for(L i=0;i<N;i++)
L N,D,A,n=0,r=0,t;V XH[200005];queue<V>P;
int main() {cin>>N>>D>>A;R{cin>>I.F>>I.S;}sort(XH,XH+N);R{while(!P.empty()&P.front().F<I.F){n-=P.front().S;P.pop();}I.S-=n;if(I.S>0){t=(I.S+A-1)/A;r+=t;P.push({I.F+2*D,t*A});n+=t*A;}}cout<<r;}