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 bisect import bisect
from collections import defaultdict

N, D, A = map(int, input().split())
XH = []

for _ in range(N):
  X, H = map(int, input().split())
  XH.append((X, -(-H//A)))

XH.sort()
Xs = [ xh[0] for xh in XH ]
HP = [ xh[1] for xh in XH ]

XR = []
for x in Xs:
  XR.append(bisect(Xs, x+2*D))

cnt = 0
temp = 0
D = defaultdict(int)

for i in range(N):
  temp -= D[i]
  HP[i] -= temp
  if HP[i] > 0:
    temp += HP[i]
    cnt += HP[i]
    D[XR[i]] += HP[i]
    HP[i] -= temp

print(cnt)