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 bisect
n, d, a = map(int, input().split())
fox = [None]*n
for i in range(n):
  x, h = map(int, input().split())
  fox[i] = (x, h)

fox.sort()
x = [int(fox[i][0]) for i in range(n)]
h = [int(fox[i][1]) for i in range(n)]

ans = 0
bit = [0]*n
for i in range(n):
  if i != 0:
    bit[i] += bit[i-1]
  if bit[i] >= h[i]:
    continue
  sub = (h[i]-bit[i]-1)//a+1
  ans += sub
  bit[i] += sub*a
  index = bisect.bisect_right(x, x[i]+2*d)
  if index == n:
    continue
  bit[index] -= sub*a
print(ans)