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 PYTHON3):

Solution:
import math
n,d,a=map(int,input().split())
XH=[]
for _ in range(n):
    x,h=map(int,input().split())
    h=math.ceil(h/a)
    XH.append([x,h])
XH.sort()
if n==1:
    print(XH[0][1])
    exit()
l=0
r=0
ans=XH[0][1]
c=XH[0][1]
L=[c]
while l<=n-1:
    left=XH[l][0]
    right=left+2*d
    if XH[r+1][0]<=right:
        cc=max(0,XH[r+1][1]-c)
        L.append(cc)
        c+=cc
        ans+=cc
        r+=1
        if r>=n-1:
            r-=1
            l+=1
    else:
        c-=L[l]
        l+=1
print(ans)