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 sys
input=sys.stdin.readline
import collections
n,d,a=map(int,input().split())
XH=[]
for i in range(n):
  XH.append([int(i) for i in input().split()])
XH.sort(key=lambda x:x[0])
D=collections.deque()
x,h=XH[0]
t=(h-1)//a+1
ans=t
D.append([x,h,t])
adj=t
for i in range(1,n):
  x,h=XH[i]
  while D:
    lx,lh,t=D.popleft()
    if lx<x-2*d:
      adj-=t
    else:
      D.appendleft([lx,lh,t])
      break
  h=max(0,h-adj*a)
  t=(h-1)//a+1
  ans+=t
  adj+=t
  D.append([x,h,t])
print(ans)