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:
def main():
  import sys
  from heapq import heappush, heappop, heapify
  input = sys.stdin.readline
  
  N,D,A = map(int,input().split())
  hq = []
  for i in range(N):
    x,h = map(int,input().split())
    hq.append((x,0,h))
  heapify(hq)

  ans = 0
  b = 0
  while(len(hq) > 0):
    x,a,h = heappop(hq)
    if a == 0:
      if b < h:
        cnt = ((h-b)+A-1)//A
        ans += cnt
        b += A*cnt
        heappush(hq, (x+2*D,1,A*cnt))
    else:
      b -= h
  
  print(ans)

if __name__ == '__main__':
  main()