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
n, d, a = map(int, input().split())
XH = [list(map(int, input().split())) for _ in range(n)]
XH.sort()
# X:座標、 C:倒すための必要爆発回数
XC = [[x, (h - 1) // a + 1] for x, h in XH]
      
q = deque([])
accum_dmg = 0
ans = 0

for x, c in XC:
  # q[-][0]は爆発が届く右端の座標
  # 爆発が届いていない地点に来たら累積ダメージを減らす
  while q and x > q[0][0]:
    _, dmg = q.popleft()
    accum_dmg -= dmg
    
  cnt = max(0, c - accum_dmg)
  ans += cnt
  accum_dmg += cnt
  
  if cnt:
    q.append([x + 2 * d, cnt])
print(ans)