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:
from collections import deque
import sys 
input = sys.stdin.readline
N, D, A = map(int, input().split())
xh = [list(map(int, input().split())) for _ in range(N)]
xh = sorted(xh)
total = 0 # 今与えているダメージの総和
D = 2*D
ans = 0
q = deque()
for i in range(N):
  x, h = xh[i]
  # 今いる場所が前回までの爆撃の範囲外になるならその分totalから引く
  while len(q) >= 1 and q[0][0] < x:
    total -= q.popleft()[1]
  h -= total

  if h > 0:
    num = (h-1)//A+1
    ans += num
    damage = num*A
    total += damage
    q += ([[x+D, damage]])

print(ans)